Artificial Plasmonic Molecules and Their Interaction ... - ACS Publications

Review Cite This: Chem. Rev. 2018, 118, 5539−5580

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Artificial Plasmonic Molecules and Their Interaction with Real Molecules Gilad Haran*,† and Lev Chuntonov*,‡ †

Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 760001, Israel Schulich Faculty of Chemistry, TechnionIsrael Institute of Technology, Haifa 3200008, Israel

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‡

ABSTRACT: Plasmonic molecules are small assemblies of nanosized metal particles. Interactions between the particles modify their optical properties and make them attractive for multiple applications in spectroscopy and sensing. In this review, we focus on basic properties rather than on applications. Plasmonic molecules can be created using either nanofabrication methods or self-assembly techniques in solution. The interaction of plasmonic molecules with light leads to excitations that are classified using the concept of normal modes. The simplest plasmonic molecule is a dimer of particles, and its lowest energy excitation takes the form of a symmetric dipolar mode. More complex excitations take place when a larger number of particles is involved. The gaps between particles in a plasmonic molecule form hotspots in which the electromagnetic field is concentrated. Introducing molecules into these hotspots is the basis of a vast spectrum of enhanced spectroscopies, from surface-enhanced Raman scattering to surface-enhanced fluorescence and others. We show in this review how these spectroscopic methods can be used to characterize the fields around plasmonic molecules. Furthermore, the strong fields can be used to drive new phenomena, from plasmon-induced chemical reactions to strong coupling of quantum emitters with the plasmonic fields. We systematically discuss these phenomena, introducing in each case the theoretical basis as well as recent experimental realizations.

CONTENTS 1. Introduction 2. Plasmonic Molecules 2.1. The Plasmonic Molecule Paradigm 2.2. Coupling between Plasmonic Excitations in Nanoparticles 2.3. Normal Modes and the Plasmon Hybridization Theory 2.4. Trimers and Larger Plasmonic Molecules 2.5. Interference Effects in Plasmonic Spectral Lineshapes 2.6. Quantum Effects in Plasmonic Molecules 2.7. Chirality Effects in Plasmonic Molecules 3. Interaction between Plasmonic Molecules and Their Neighbors 3.1. Surface-Enhanced Raman Spectroscopy As a Probe of Plasmonic Fields 3.2. Surface-Enhanced Raman Spectroscopy As a Probe of Chemical Reactions 3.3. Surface-Enhanced Fluorescence, Infrared Absorption, and Nonlinear Optical Signals 3.4. Strong Coupling of Plasmonic Molecules and Quantum Emitters 4. Conclusions and Outlook Appendix: Some Introductory Comments on the Methodology Used for Studying Plasmonic Molecules

© 2018 American Chemical Society

A.1. Theoretical Methods: Mie Theory and the Static Approximation A.2. Theoretical Methods: Plasmon Hybridization A.3. Theoretical Methods: Symmetry Analysis A.4. Experimental Methods: Optical Spectroscopy of Individual Plasmonic Molecules A.5. Experimental Methods: Spectroscopy within the Electron Microscope Associated Content Special Issue Paper Author Information Corresponding Authors ORCID Notes Biographies Acknowledgments References

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1. INTRODUCTION The constant demand for device miniaturization as well as for improving the resolution and lowering the detection limit in spectroscopic measurements initiated an extensive research in the field of plasmonics.1−7 Conduction electrons on a metal surface, driven by the electromagnetic field of light, enhance the

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Received: October 27, 2017 Published: May 21, 2018 5539

DOI: 10.1021/acs.chemrev.7b00647 Chem. Rev. 2018, 118, 5539−5580

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Figure 1. Plasmonic atoms: resonances in subwavelength nanoparticles. (a) Schematic representation of the collective oscillations of the conduction electron cloud on the surface of noble metal nanoparticle, forced by the electric field of light. Reprinted with permission from ref 56. Copyright 2003 American Chemical Society. (b) Charge distributions on the surface of a sphere corresponding to the normal modes with angular momentum quantum numbers l = 1, 2, and 3. (c) The complex-valued dielectric function of silver, which gives rise to the surface plasmon resonances. This data is reproduced from ref 57. Copyright 1997 Elsevier Inc. (d) (top) Scanning electron microscopy (scale bar, 200 nm) and optical dark-field images of plasmonic nanoparticles. Reprinted with permission from ref 58. Copyright 2007 Wiley-VCH Verlag GmbH & Co. (bottom) Dark-field images of collected from nanoparticles in air (left panel) or immersed in oil (right panel). Reprinted with permission from ref 59. Copyright 2003 American Chemical Society.

field locally up to several orders of magnitude. The region where the field is concentrated is typically as small as only a few nanometers, which provides a unique opportunity to manipulate the electric field of light with a spatial resolution of 2−3 orders of magnitude below the diffraction limit. The effect of the field enhancement was first identified in the context of surface enhanced Raman scattering (SERS) from molecules adsorbed on the surface of roughened metal electrodes or dissolved in colloidal solutions of metal particles (sols).8−12 The mechanism of such enhancement was predicted early on to originate in the near-fields induced at the interparticle gaps within the colloidal aggregates.13 However, because the experimental data then available involved a wide distribution of aggregates of different sizes and shapes,14 the correlation between their optical (near-field) properties and SERS signals was highly challenging.15,16 Additional processes associated with chemical interaction between the metal surface and adsorbed molecules, contributing along with the electromagnetic effect, were initially thought to provide the dominating mechanism for signal enhancement.9,17−19 Optical spectroscopy of sols before and after induced aggregation together with theoretical modeling of their optical properties indicated formation of clusters of nanoparticles, which showed up as spectral broadening and the appearance of new red-shifted peaks.20−23 More detailed single-molecule SERS studies combined with dark-field spectroscopy as well as atomic force and electron microscopy overcame the limitations of the ensemble studies and established a direct connection between the SERS signal enhancement and the surface plasmon spectrum of nanoparticle clusters.24−30 In the modern terminology, nanoparticle clusters are thought of as optical antennas that receive and transmit the light from the farfield to the near-field and back.4,31−33 Effective operation of

such optical antennas is achieved by rational design of the nanoparticle cluster geometry, which shapes both the near-field and the far-field of the cluster.34,35 Surface-plasmon based antennas need not be limited to selfassembled random clusters of particles, as discussed above. In fact, research in recent years has focused on the formation of more ordered arrangements of particles, involving either solution-prepared or nanofabricated structures. Such welldefined assemblies of particles that sustain surface-plasmon resonances are often called “plasmonic molecules” and are the topic of this review. By necessity, we will sometime have to discuss the individual constituents of plasmonic molecules, which we will therefore call “plasmonic atoms”. Traditionally, plasmonic atoms have been prepared from coinage metals, mostly silver and gold. The size and shape of plasmonic atoms synthesized in solution can be rationally controlled via the preferential growth of the desired crystallographic planes, which is achieved by sophisticated manipulation of the interaction between the metal atoms on the nanoparticle surface, carefully selected ligand molecules, and reducing agents.36−39 The ensuing plasmonic atoms can be used as is or serve as the basis for the formation of plasmonic molecules, either in solution or on a surface. In addition to solution techniques, a broad range of nanofabrication methods40 have also been used to prepare plasmonic molecules. For example, precise control over their size and shape can be achieved using optical and electron-beam lithography,41 nanosphere lithography,42 and nanostencil lithography.43 Multiple additional methods for the controlled fabrication of plasmonic molecules were also developed, including those based on the action of capillary forces on the surface,44 optical forces applied by the electric field of the laser light45−47 or the field of an electron beam,48 mechanical forces applied by a direct manipulation 5540


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with a tip-based scanning microscope,49,50 DNA origami,51 and others. This review starts with a discussion of the optical properties of the individual nanoparticles, plasmonic atoms. We continue to the properties of combinations of these atoms, plasmonic molecules, and discuss them using approaches borrowed from molecular spectroscopy, which include hybridization of states and a group theoretical description based on symmetry. We address in detail the consequences of interparticle interactions as they are manifested in the optical properties related to the enhanced near- and far-fields associated with a plasmonic molecule. Next, we move to discuss experiments conducted with molecules located within the enhanced field regions, which can now be intuitively interpreted based on similar concepts. Multiple applications of plasmonic molecules have been proposed over the years, from surface-enhanced spectroscopy to photochemistry and catalysis. The detection limit was pushed to the level of a single molecule and extended from linear to nonlinear spectroscopic experiments. The interaction between hot electrons generated in plasmonic structures with molecules located on their surface was shown to lead to chemical transformations impossible by standard chemical methods. Hot electrons generated by plasmonic molecules were employed in various applications, including imaging and cancer therapy. In certain cases, the strength of the enhanced fields was shown to be sufficient for strong coupling to individual emitters located in their vicinity. This finding may serve as a platform for plasmonic quantum devices operating on the nanoscale. The review will discuss many of these phenomena from the point of view of the plasmonic molecule and will highlight the most important findings in this burgeoning field in recent years. The Appendix includes some introductory materials describing both theoretical and experimental methods used to study plasmonic molecules, which might help the novice in reading the review. It is important to note that we cannot and do not make an attempt to be fully comprehensive in covering all types and shapes of plasmonic molecules and their applications that were discussed in published work, as the relevant literature is enormous. We apologize to any colleague whose work is not cited or not fully represented in the review.

rectangular prisms, cubes, rods), but having dimensions that are sufficiently subwavelength, can in many cases be regarded as point dipoles, thereby also falling under the paradigm of the plasmonic atom.54,55 In an assembly of two or more plasmonic atoms, the particles are located at a small-enough distance from each other for the Coulomb interaction between their conduction electrons to become noticeable.13 Such a nanoparticle cluster features a molecule-like behavior. Indeed, the plasmon modes of individual nanoparticles hybridize to form the new normal modes of the cluster, just like atomic orbitals hybridize to form new molecular orbitals when chemical bonds are established.60−62 Another molecular analogy is found in the interaction between molecular chromophores located close to each other and having similar excitations. Collective excitations of nanoparticle clusters are analogous to the new exciton states formed upon interactions between the chromophores.63 The new molecule-like plasmon modes follow the rules of symmetry, and their optical properties are well-described with concepts from group theory familiar to the molecular spectroscopist.64−68 Optically allowed and forbidden modes emerge and, when they spectrally overlap, they may feature interesting phenomena such as Fano-like interferences, analogous to the effects observed in atomic and molecular spectroscopy for bound states embedded within a continuum.69 Modern methods of nanotechnology allow the fabrication of a large variety of three-dimensional subwavelength structures made of plasmonic atoms.70−72 Here, additional molecular concepts like aromaticity (involving ring currents) and chirality (handedness) become relevant. Finally, structures with systematically repeating motives, plasmonic polymers, as well as large aggregates with optical properties resembling those of disordered matter, all have their direct molecular or sometimes solid-matter-like analogues.73−79 To discuss the properties of plasmonic molecules, the way they interact with quantum objects (molecules, nanoparticles etc.) in their vicinity, and how they can be used to manage near-fields and transmit signals to the far-field for detection, we shall consider first and in some detail the key experimental observations and theoretical developments that have led to the formulation of the concept.

2. PLASMONIC MOLECULES 2.1. The Plasmonic Molecule Paradigm

2.2. Coupling between Plasmonic Excitations in Nanoparticles

Individual spherical noble metal nanoparticles have been termed “plasmonic atoms”, a name that stems from the analogy between the electron angular momentum states in a singleelectron atom and the normal modes of the collective excitations of conduction electrons on the surface of the particles (schematically shown in Figure 1), known as localized surface plasmons (LSP).52,53 The origin of this analogy is the spherically symmetric geometry in both cases. When the nanoparticle dimensions are small (on the order of a few nanometers to a few tens of nanometers), the energies of the corresponding plasmonic normal modes fall in the visible spectral range and they can be excited by light. The exact position of the LSP resonance depends on the dielectric function of the constituent metal and of the environment (Figure 1c,d). Because of the symmetry of the electromagnetic field of the light, the most efficient excitation is associated with the l = 1 (dipolar) plasmonic mode (the lowest normal modes are illustrated in Figure 1b). Nanoparticles of shapes other than spherical (e.g., oblate and prolate spheroids, triangular and

Probably the most influential fundamental study of the interaction between electromagnetic radiation and spherical objects is the 1908 work of Mie,80 who presented a solution to this radiation scattering problem as an expansion in a series of spherical functions about the size parameter mx, where x = ka, k is the wavenumber of the electromagnetic wave, a is the radius of the sphere, and m is the ratio of the refractive indices of the metal sphere and its dielectric environment (see more details in section A.1. of the Appendix). For individual nanoparticles of subwavelength dimensions mx ≪ 1 and therefore the full solution for the electromagnetic field they absorb or scatter reduces to the leading term of the expansion, which corresponds to the dipolar surface charge distribution.81 The resulting expression for the particle polarizability is formally similar to the Clausius−Mosotti (or Lorentz−Lorenz) formula for the polarizability of a sphere in a static electric field, denoted by α in eq A.5, section A.1 of the Appendix. Indeed, when the variation of the field is negligible across the nanoparticle, the 5541


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Figure 2. Multipolar excitations in plasmonic nanoparticles beyond the electrostatic limit. (top) Extinction spectra of ensembles of silver nanoparticles of increasing sizes. The mean nanoparticle sizes are indicated. As the particle size increases, the spectra red-shift broaden. (bottom) The corresponding electron micrographs of the particles. Reprinted with permission from ref 92. Copyright 2004 American Chemical Society.

generalizes the Mie theory to cases of multiple spheres, the so-called Generalized Mie Theory, facilitates evaluation of the changes in charge distribution and the associated optical properties.14 Because solutions for the charge distribution on the surface of interacting spheres are naturally expanded in the single-sphere normal modes, higher mode orders are required to describe stronger interactions between particles, even when they are significantly smaller than the wavelength of light. Therefore, generally, the simple picture of interacting point dipoles can be adopted only within the known limitations of the lowest-order approximation. Nevertheless, such a dipolar picture provides great intuition and general guiding lines for experimental design.14 Systematic dark-field spectroscopy studies of the dependence of interparticle interactions on the distance between two nanoparticles were conducted with gold nanoparticle dimers fabricated with electron-beam lithography.93−97 Experiments conducted by Schultz and co-workers have shown that for interparticle distances of the order of nanoparticle size, the plasmon spectral peak, excited with the light polarized along the dimer axis (longitudinal polarization), red-shifts exponentially with a decrease in the interparticle distance.93 Rechberger et al. have found that at the same time, for the light polarized perpendicular to the dimer axis (transverse polarization), the plasmon resonance shifts to the blue.97 Similar trends were obtained by Moerner and co-workers in their studies of bowtie antennas.94 Some typical scattering spectra of plasmonic dimers are shown in Figure 3a.95 The above observations match the expectation based on Coulomb interaction between the surface charge distributions. Considering for simplicity only the dipolar contribution, at any instant of time the two dipoles induced along the dimer axis are aligned in the same direction and parallel to this axis. In this configuration, the electrostatic energy of interaction is lowered for smaller interdipole

electrostatic approximation holds, as can be assumed in the context of SERS and localized plasmon sensing.56,82 The expression for dipolar polarizability renders the principle of plasmon dielectric sensing in simple terms. In the vacuum (εm = 1), the plasmon resonance of the nanoparticle appears at the pole of α when the real part of the metal dielectric function (ε) approaches −2 (see Figure 1c for the case of silver). In the absence of resonances associated with the dielectric environment, i.e., normal dispersion, the spectral position of the plasmon resonance experiences a gradual red-shift for increasing values of the effective permittivity of the nanoparticle environment, as seen in Figure 1d. This effect, which is a manifestation of the metal surface-charge screening by the bound charges of the dielectric environment, was extensively studied and is broadly used in various sensing scenarios.1,83−88 As a nanoparticle’s size becomes larger, radiation damping (i.e., loss of the excitation energy to radiation) leads to broadening of the plasmon line shape, while the dynamic depolarization effect leads to a red-shift of the resonance peak,89 as seen in the spectra of Figure 2. Because of the symmetry of the electric field of light, it cannot directly excite multipole orders higher than dipolar (quadrupole, octupole, etc.) in small nanoparticles. Typically, however, they are excited via retardation effects in larger nanoparticles, which appear because the finite nanoparticle size approaches the wavelength of the light, to be compared to the retardation-free electrostatic limit valid for small (point-like) nanoparticles.90,91 Higher multipole excitations appear as additional peaks in the optical spectrum in Figure 2.92 When two or more nanoparticles are brought sufficiently close to each other to form a cluster, the Coulomb interaction between the surface charges of the particles becomes strong enough to alter their distribution. When spherical nanoparticles are considered, the theoretical description that formally 5542


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Figure 3. Plasmonic molecules: nanoparticle dimers. (a) Scattering spectra collected with two orthogonal light polarizations (as indicated by arrows) from silver nanoparticle dimers (D = 95 nm, h = 25 nm) with different interparticle gaps d ≈ (A) 10, (B) 15, (C) 25, (D) 50, and (E) 250 nm. Spectrum F from a single nanoparticle is included for comparison. Reprinted with permission from ref 95. Copyright 2005 American Chemical Society. (b) Near-field maps of the electric-field enhancement around a dimer of 36 nm particles with a 2 nm interparticle gap, excited at 430 nm and 520 nm with polarization along the dimer axis. Spectra measured with light both parallel and perpendicular to the dimer axis are shown in the upper panel. Reprinted with permission from ref 103. Copyright 2004 American Institute of Physics Publishing LLC.

dependence of the plasmon resonance spectral shift on the interparticle size and distance.100,101 They found that when the spectral shift is normalized by the resonant wavelength, and the interparticle distance is normalized by the nanoparticle size, a simple plasmon-ruler expression can be obtained, which is independent of nanoparticle size, shape, metal type, or medium dielectric constant. While for large interparticle separations the results could be well-described by dipolar interactions, Schatz and co-workers have shown that higher-order terms are important for quantitative description of plasmon spectra from dimers with smaller interparticle distances.95,102,103 The latter scenario is especially important because it leads to strongly enhanced near fields in the nanoparticle gaps, as shown in Figure 3b. Khlebtsov et al. systematically compared plasmon spectra of dimers with various interparticle distances as obtained within the dipolar approximation or full electrodynamic calculations including all multipole orders and demonstrated the large importance of the latter for the accurate description of the plasmon fields.104 Classical electromagnetic theory can, in general, be used not only to calculate spectra but also to fully map the enhanced near-fields around plasmonic nanostructures, given that the geometry of the plasmonic molecules is known.105,106 To facilitate experimental studies of the surface charge distributions

distances, leading to the observed red-shift of the plasmon resonance. On the other hand, for light polarized normal to the dimer axis, the individual dipoles are both oriented in this direction such that the interaction energy increases for smaller distances, leading to a blue-shift. The energy of the interaction of the two dipoles induced on the surfaces of the individual nanoparticles upon excitation scales as d−3, where d is the distance between the particle centers (effective-dipole locations). Because in the dipole limit the individual nanoparticle dipole strength depends on the single-particle polarizability, which scales as a3, where a is the size of the nanoparticle (see section A.1), the interparticle interaction strength scales in fact like ∼ (a/d)3. Such an interaction has a significantly longer range than, for example, the dipole induced-dipole interaction in Förster resonance energy transfer (FRET). Plasmonic molecules were therefore suggested to serve as nanoscale rulers, outperforming conventional molecular chromophore-based rulers used in FRET in terms of signal strength, stability, and distance range. Alivisatos and colleagues used pairs of gold and silver nanoparticles attached to complementary DNA strands to measure DNA hybridization dynamics by following the spectral shift of the plasmon resonance resulting from the interparticle interaction at distances as far as 70 nm.98,99 El-Sayed and co-workers derived an empirical universal scaling law to describe the 5543


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Figure 4. Plasmon hybridization theory and optical properties of heterodimers. (a) Plasmon mode hybridization scheme (top) and interparticle distance dependence of the energy of hybridized modes (bottom). The symmetry labels of the hybridized modes and the corresponding magnetic quantum numbers of the parent single nanoparticle modes are indicated. Reprinted with permission from ref 130. Copyright 2007 American Chemical Society. (b) Scanning electron micrographs of heterodimers, scale bar is 200 nm. (c) Plasmon scattering spectra of heterodimers for different direction of excitation light propagation, as indicated schematically by arrows of matching colors. The lowest dimer composed of a solid sphere and a nanoshell features the “optical nanodiode effect”. Reprinted with permission from ref 129. Copyright 2010 American Chemical Society.

interparticle gap, indicated that for small distances, the interparticle interaction dramatically exceeds the limit of dipole coupling, and the induced charge distribution on the nanoparticles’ surfaces within the gap has a complex pattern.114 Similar patterns, which could be described by admixture of higher multipole orders, are expected from a plasmon hybridization analysis, as discussed in section 2.3 below.61 The amplitudes and phases of the electric field around plasmonic molecules resonant in the mid-infrared were measured using near-field microscopy by Hillenbrand and coworkers,115 who found a good agreement with the classical prediction. Interestingly, the near-field spectrum is typically red-shifted as compared to the far-field scattering spectrum of the plasmonic molecules.116−118 A simple oscillator model by Zuloaga and Nordlander qualitatively rationalized this result, identifying the far-field scattering with the power absorption of the oscillator, which peaks at the resonance frequency, while the near-field, identified with the amplitude, is red-shifted due to damping.119 Katz et al. extended this model to explicitly include radiation damping effects.120

and the near-fields around plasmonic molecules, fabrication methods that enable reliable production of small interparticle distances to the desired precision are required. Various experimental approaches were developed to attempt reproducible large-scale fabrication of plasmonic molecules possessing small gaps, including among others photochemical metal deposition, utilization of DNA templates, and electrostatic self-assembly.107−109 Interestingly, the latter method was used by Lloyd et al.110 to facilitate assembly of nanoparticles capped with ligands of alternating surface charges for the experimental realization of a plasmonic lens from self-similar spheres, following the original design of Li et al.,111 who suggested it as a means to get a particularly high enhancement. Further discussion of the assembly of plasmonic molecules with small gaps can be found in section 3.1, where the application of molecules as probes of the near fields in these gaps is examined. Near-field imaging techniques112 can in principle directly resolve the enhanced fields in the gaps of plasmonic molecules, although their application to this problem is highly challenging. A near-field optical imaging study of nanocube dimers by Kim et al.,113 aimed at mapping the field enhancement within the 5544


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Figure 5. Electron energy loss spectroscopy (EELS) and plasmon modes. (a,b) Spectra collected from a spherical silver nanoparticle (a) and a nanoparticle dimer (b) with different positions of the excitation electron beam. The excitation positions are indicated on the corresponding scanning electron micrographs. Reprinted with permission from ref 131. Copyright 2009 American Chemical Society. (c) Spectrum of a silver nanocube and (d) 3D tomographic reconstruction of electron densities corresponding to labeled peaks in the spectrum. Reprinted with permission from ref 137. Copyright 2013 Nature Publishing Group.

Another useful tool for mapping the plasmon fields around particle clusters is electron energy loss spectroscopy (EELS).121−123 The very small spot size of the electron beam and the availability of the appropriate instrumentation for monochromatic detection allow for a detailed spatial mapping of plasmon fields at each loss energy. Such a mapping readily reveals the corresponding density of the photonic states of the cluster124 with subnanometer resolution125,126 (more details on the STEM-EELS methodology are given in the Appendix, Experimental Methods section A.5.).

particle), which can be intuitively visualized, as was suggested by Kreibig.14,128 Nordlander and co-workers developed a plasmon hybridization theory,60 which allows to systematically construct the normal modes of interacting nanoparticles and calculate their corresponding energies with the number of terms in multipole expansion set to the required precision of the calculation (see Appendix, Theoretical Methods section A.2 for details). For example, they have shown61 that longitudinal dipolar symmetric and antisymmetric modes split and shift to lower and higher energies, respectively, as the interaction strength increases for smaller interparticle distances, as illustrated in Figure 4a. Adopting the terminology from molecular spectroscopy, optically bright longitudinal symmetric modes were referred to as the bonding modes of plasmonic molecules, while dark antisymmetric modes were referred to as antibonding. For more strongly interacting nanoparticles (smaller interparticle distances) the bonding (antibonding) modes red-shift (blueshift), and their optical scattering cross sections typically increase. In dimers made of two identical nanoparticles, symmetric and antisymmetric modes do not interact with each other because they belong to different irreducible representations (more details on the group theorerical approach to plasmonic molecules are given in the Appendix, Theoretical Methods section A.3). Therefore, the corresponding energy curves plotted versus interparticle distance can cross each other. On

2.3. Normal Modes and the Plasmon Hybridization Theory

Because plasmon excitations in individual nanoparticles are associated with the corresponding normal modes (such as those described by the multipole expansion in the case of spherical particles), it is useful to describe plasmon excitations in clusters of N particles with the (2l + 1)N collective normal modes constructed from linear combinations of the normal modes of individual nanoparticles. This description of the plasmonic excitations of nanoparticle clusters was already compared above to the description of molecular orbitals and is also very similar to the description of vibrational excitations in molecules.127 For the case of a dimer, N = 2, the cluster modes are the symmetric and antisymmetric combinations of the individual nanoparticle modes. When small nanoparticles and large interparticle distances are considered, the excitation is dominated by contributions from the six dipolar modes (three for each 5545


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Figure 6. Nanoparticle trimers. (a) Symmetry-adapted linear combinations (SALCs) of the plasmonic modes of a trimer of D3h symmetry, obtained using group theory. The symmetry labels of the corresponding irreducible representations are shown. Reprinted with permission from ref 64. Copyright 2006 American Chemical Society. (b) Scattering spectrum of an array of silver D3h trimers fabricated by electron beam lithography. SEM image of a representative trimer is shown on top, and the distribution of the near-field at the resonance wavelengths is plotted in the middle panel, showing correspondence to the bonding and antibonding E′ SALCs in panel a. Reprinted with permission from ref 145. Copyright 2008 American Chemical Society.

order modes in dimers results in plasmon excitation by light in the spectral region of the higher-energy antisymmetric dipolar modes. The plasmon hybridization approach is well suited to analyze the corresponding interactions and was demonstrated in multiple studies to be very useful to interpret experimental results. A strong validation for the plasmon hybridization approach was provided by EELS experiments on nanoparticle dimers and bowtie antennas of different configurations.131−133 The selection rules for excitation by an electron beam are different than the selection rules for excitation by light.134 This opens an opportunity to excite optically dark plasmon modes. Indeed, the optically dark antisymmetric dipolar modes of a dimer could be directly observed when the electron beam passed through the gap between the paraticles, as shown in Figure 5a,b.131 Recently, Quillin et al. obtained energy loss spatial maps of all relevant normal modes of a nanoparticle dimer with a remarkable quality.135 Barrow et al. went further and mapped the spatial distribution of plasmon fields in short linear chains

the other hand, in heterodimers, composed of nanoparticles of different size or shape as those shown in Figure 4b, Brown et al.129 find that the lack of mirror symmetry leads to coupling between all modes. Consequently, mode admixtures and avoided crossing behavior (mutual “repulsion” of the energy curves rather than crossing) appear when the interparticle interaction becomes stronger, as happens for smaller interparticle distances. In addition, the symmetric and antisymmetric modes of the dimer have different excitation cross sections for different directions of excitation light (from either the side of the sphere or the side of the nanoshell). These modes can thus be excited preferentially, leading to an “optical nanodiode effect”, i.e., to a significant dependence of the optical response on the light propagation direction, as seen in Figure 4c. This effect can be found useful in the development of nanoscale photonic switches.129 In small but strongly interacting nanoparticles, the higherorder modes of one nanoparticle can mix with the dipolar modes of other nanoparticles.14,61 Such an admixture of higher5546


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Figure 7. Symmetry breaking in nanoparticle trimers. (a) Plasmon scattering spectra of silver trimers generated by assembly of spherical nanoparticles. SEM images of the corresponding trimers are shown in the inset. The red and blue lines correspond to excitation with light polarized parallel and perpendicular to the trimer’s base. The green line corresponds to excitation with nonpolarized light. The symbols of the symmetry point groups and irreducible representations associated with the main peaks in the spectra are shown. (b) Symmetry correlation table for the in-plane plasmon modes of a trimer: schematic representation of the evolution of dipolar SALCs as the symmetry is broken gradually by opening the trimer’s vertex angle; (left column) SALCs of a D3h trimer; (middle column) evolved SALCs of a C2v trimer; (right column) the corresponding SALCs of a linear trimer. Reprinted with permission from ref 65. Copyright 2011 American Chemical Society.

of up to five nanoparticles, which further illustrated how the individual nanoparticle modes hybridize and develop into collective excitations.136 The classical electromagnetic approach and in particular the plasmon hybridization method break down at very small interparticle distances, where the interaction between the electron wave functions of different nanoparticles has to be considered on the quantum mechanical level (see a detailed discussion of quantum effects in section 2.6). High-resolution STEM-EELS experiments by Duan et al. established that, in nanoparticle dimers, the classical description is valid for interparticle distances as small as 0.5 nm,133 making the plasmon hybridization approach virtually universally appropriate for colloidal systems, where such interparticle distances are dictated by the presence of ligand molecules capping the nanoparticles. Another limitation of the quantitative application of the plasmon hybridization method is encountered when individual nanoparticles forming plasmonic molecule have highly irregular shapes. In such cases, a detailed picture of the plasmon modes and their charge distribution across the nanoparticle surfaces within the gap can be obtained from 3D maps constructed by means of STEM-EELS plasmon field tomography.138−140 Progress in this direction includes studies of plasmon

excitations in nanoparticle cubes (see Figure 5c,d) and cuboid dimers.137,141 As a final note, we would like to mention that, while the plasmon hybridization approach provides an intiuitive chemist’s perspective on plasmonic molecules, an alternative perspective, rooted in electrical engineering and based on the theory of electrical circuits, was introduced by Engheta and co-workers.142 In one example of the application of this approach, Shi et al. studied the spectra of combinations of plasmonic and dielectric particles.143 They classified the plasmonic nanoparticles as equivalents of inductors, and the dielectric nanoparticles, as equivalents of capacitors, and used the corresponding nanocircuit models to interpret their optical properties. 2.4. Trimers and Larger Plasmonic Molecules

Clusters of three and four nanoparticles have also been analyzed using the plasmon hybridization theory.64,144 Here it was also found that an approach adapted from molecular spectroscopy, based on group theory, can be used to construct and analyze the normal modes of such clusters.64 Within the group theory formalism, the normal modes are associated with the irreducible representations of the relevant symmetry point group and can be constructed as symmetry-adapted linear 5547


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Figure 8. Nanoparticle tetramers. (a) Structure of three different tetramers, obtained by bright-field and dark-field electron microscopy. (left) 2D C2v tetramer, (middle) 2D D2h tetramer, (right) 3D C2v tetramer. Scale bars are 50 nm. (b) Experimental and simulated EELS maps of the tetramers of panel a at the indicated energies. The identity of the SALC(s) relevant for each map is (are) indicated above it. Reprinted with permission from ref 67. Copyright 2016 American Chemical Society.

these degenerate modes. It is important to note the nice correspondence found between the near-field maps calculated at the resonance wavelength of the D3h trimer using electromagnetic simulations, as shown in Figure 6b, and the shapes of SALCs. The symmetry-based analysis was further used in multiple experimental studies of optical properties of small aggregates by Chuntonov and Haran65,66,146−148 as well as by others.67,68,149−153 Hopkins et al. showed theoretically that a polarization-independent response is expected for rotationally symmetric plasmonic molecules.150 Indeed, Kim et al. studied assemblies of highly uniform spherical nanoparticles and found a good agreement between the experimental results and the normal mode-based interpretation.154 However, Rahmani et al. cautioned, based on their experimental results, that similar polarization-isotropic far-field responses can be the outcome of very different different near-field patterns.155 The symmetry-based approach provides intuitive means to understand plasmon normal modes not only in nanoparticle clusters of high symmetry but also in clusters where the symmetry is broken. Chuntonov and Haran studied experimentally the evolution of plasmon modes following a gradual breaking of the symmetry in nanoparticle trimers.65,66 Figure 7 demonstrates symmetry breaking of a D3h trimer by opening

combinations (SALCs) of individual nanoparticle normal modes. SALCs were constructed for a trimer made of identical spherical nanoparticles arranged in a symmetric configuration, where the lines connecting the nanoparticle centers form an equilateral triangle.64 Such a trimer belongs to the D3h point group, and its SALCs are shown in Figure 6a. As expected, on the basis of the basic tenets of group theory, analysis of normal modes obtained from plasmon hybridization theory for these clusters showed that dipolar modes mix only with higher-order modes of the same irreducible representation.64 These theoretical ideas were put to experimental test in several works. Käll and co-workers have studied plasmon spectra of lithographically manufactured equilateral trimers of silver nanoparticles and found that plasmon spectra are insensitive to the polarization of the excitation light propagating normal to the sample surface (Figure 6b).145 Their result is understood within the framework of SALCs: in clusters of the D3h symmetry, because of the presence of the C3 rotation axis, doubly degenerate optically bright E′ irreducible representations are obtained. The corresponding lowest-order dipolar SALCs have their total in-plane dipole moments orthogonal to each other and equal in magnitude. Thus, any in-plane excitation can be decomposed into a linear combination of 5548


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Figure 9. Nanoparticle oligomers. (a) Scanning electron micrographs of a series of plasmonic molecules constructed with the template-guided surface self-assembly method. Scale bars correspond to 50 nm. Reprinted with permission from ref 149. Copyright 2011 American Chemical Society. (b) (left) Scanning electron micrographs of naphthalene-like plasmonic molecules fabricated by electron-beam lithography. (right) Experimental and theoretical extinction spectra of the plasmonic molecules. (bottom) Charge density and magnetic field plots at resonances I and II. The magnetic nature of mode II is emphasized by the arrows showing the direction of the electric field. Reprinted with permission from ref 162. Copyright 2012 American Chemical Society.

one of its vertex angles.65 As the C3 rotational symmetry of the trimer is broken, the degeneracy of the E′ irreducible representations of the D3h group is lifted, and they transform into A1 and B2 representations, as observed in experimental spectra (Figure 7a). The gradual evolution of all normal modes of the trimer is demonstrated in the correlation table of Figure 7b. Interestingly, the lowest energy mode of the symmetric trimer is dark and has a ring-like structure. When the symmetric trimer is transformed first into a C2v structure and then into a linear structure of D∞h symmetry, it is this dark mode that develops into the single bright bonding mode of the cluster. Similar trends were observed also when a trimer’s symmetry

was broken by gradually decreasing the size of one particle (in a series that ended with a dimer) or the size of two of the particles (in a series that ended with a single particle).66 Understanding the transformations between optically bright and dark plasmon modes in trimers, as illustrated in Figure 7, led to a detailed understanding of origins of the polarization dependence in optical spectra, paving the way to use trimeric clusters as nanoscale devices to control light polarization.147,148,156,157 Barrow et al. used similar ideas on the symmetry correlation of plasmon modes in their recent EELS study of plasmon trimers and tetramers constructed by DNA-directed self5549


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Figure 10. Plasmonic polymers and nanoparticle chains. (a) Scheme of the plasmonic nanoparticle polymerization method developed by Kumacheva and co-workers, showing different scenarios of polymer-directed controlled assembly of nanoparticle aggregates. Scale bars depict 100 nm. Reprinted with permission from ref 165. Copyright 2007 Nature Publishing Group. (b) Optical properties of linear nanoparticle chains: (left panel) extinction spectra of the chains, whose scanning electron micrographs are shown; (right panel) dependence of extinction peak wavelength on the chain length, with results from a generalized Mie theory (GMT) calculation shown as a continuous line. Reprinted with permission from ref 163. Copyright 2014 The Royal Society of Chemistry.

assembly.67,68,158 They followed the transformation between the modes in planar plasmonic molecules of point groups with gradually decreasing symmetries: D∞h, D4h, D3h, D2h, and C2v, as illustrated in Figure 8. The observation of both bright and dark modes in EELS experiments and their gradual evolution with the change of cluster geometry nicely complemented optical studies and strongly supported the validity of the approach based on symmetry correlation. Plasmonic molecules with a larger number of plasmonic atoms can also be fabricated and studied (Figure 9).149 Liu and co-workers probed the optical properties of plasmonic molecules designed in the shape of conjugated rings like benzene, fabricated by electron beam lithography.159,160 They followed the transition between individual nanoparticle modes and collective modes as the distances between particles were reduced. Ring-like modes, frequently referred to as “magnetic,” were observed in heptamers of the D6h point group.161 These modes are similar to the lowest energy dipolar normal mode of a nanoparticle trimer with D3h symmetry, which exhibits a ring-like arrange-

ment of individual nanoparticle dipole moments and is also dark.64 Liu et al. fabricated a series of larger plasmonic oligomers by fusing heptamer rings into structures resembling aromatic molecules of naphthalene, anthracene, and so forth.162 They found that in such extended “aromatic” structures, magnetic dipoles of adjacent rings are pointing in opposite directions. As a result, these modes were suggested as potential candidates for low-loss propagation of electromagnetic excitation to distances as long as several microns.163 Nanoparticle chains may also serve as candidates for the implementation of subdiffraction limit waveguiding.164 Such structures were termed by Link and co-workers “plasmonic polymers.”76 They can be built, for example, by a recently developed nanoparticle self-assembly method involving hydrophobic and hydrophilic interactions between appropriately selected capping polymer layers (see Figure 10a for this fabrication scheme)165−167 as well as by taking advantage of the action of capillary forces.168 Plasmon spectroscopy experiments conducted on linear nanoparticle chains by Mulvaney and co5550


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Figure 11. Disordered plasmonic polymers. (a) Theoretical maps of the near-field distributions at two different excitation wavelength. A delocalized excitation at 850 nm (left panel) and a localized excitation at 645 nm (right panel) are shown. Reprinted with permission from ref 172. Copyright 2012 American Chemical Society. (b) Experimental EELS maps of plasmon excitations in a disordered fused nanoparticle chain: (left panel) map of the delocalized mode collected at 2.4 eV; (right panel) a localized mode, collected at 0.79 eV. Scale bar 50 nm. Reprinted with permission from ref 173. Copyright 2015 Nature Publishing Group. (c) Theoretical modeling suggests that the details of facet-to-facet interactions of nanoparticles in chains are important in determining their optical properties. Reprinted with permission from ref 174. Copyright 2017 Optical Society of America.

workers169 and by Reinhard and co-workers170 showed that for a particle size of 50−100 nm, the lowest energy longitudinal optically bright bonding plasmon mode of the chain undergoes a red-shift with an increasing number of the nanoparticles, which converges to the limit of the infinite chain already for 5− 10 particles. Link and co-workers163 conducted a systematic study of this phenomenon by using longer chains of nanoparticles of various sizes and found that it is the number of nanoparticles in the chain, rather than its length, that is the most important factor defining the infinite chain limit, as seen in Figure 10b. On the other hand, the overall size of the plasmonic polymer, including also its geometrical width, strongly influenced the resonance line width, as it is linked to the retardation of the electric field of light. By further increasing of the number of nanoparticles in selfassembled structures, and placing them stochastically, one can form disordered planar aggregates. Propagation of optical excitations in disordered matter is an active field of research in solid-state physics,171 whose general ideas can be potentially extended into the field of plasmonic molecules. In theoretical studies, Esteban at al.172 identified that such disordered aggregates of ca. 100 nanoparticles support both extended-

chain like plasmon modes, resembling those found in linear chains, and more localized excitations, as shown in Figure 11a. Teulle et al. conducted an EELS study on fused nanoparticle chains and identified both delocalized and localized modes at different plasmon excitation energies (see Figure 11b).173 Interestingly, these modes were found to be robust to a certain degree of imperfection of the linear geometry, while at the same time very sensitive to the individual nanoparticle curvature, e.g., round surfaces of spheres vs flat ones of cubes, as shown in Figure 11c.174 These chain-like modes, therefore, appear to be an essential element required to understand the behavior of complex plasmonic clusters. So far we discussed only two-dimensional plasmonic molecules. Various methods of planar cluster fabrication were used to generate these structures, from stochastic assembly approaches to deterministic methods. The former included, for example, solution phase aggregation followed by the deposition on a planar substrate and capillary-force guided selfassembly.65,149,175 The latter involved electron beam lithography95 and direct manipulation with an AFM tip49,176 or an electron beam.48 Three-dimensional plasmonic molecules can also be fabricated,68,71,72 and special electromagnetic properties 5551


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Figure 12. Magnetic modes in plasmonic molecules. (a) A tetrahedral cluster shows a magnetic response: (left) predicted extinction and absorption spectra of the cluster, with electric−dipole and magnetic−dipole resonances marked; (right) field profiles at the two resonance wavelength are shown. Color depicts the intensity of the out-of-plane magnetic field HZ in the plane containing the centers of three spheres; (arrows) in-plane electric induction (Dx, Dy) in the same plane. Note the strong magnetic field in the right profile. Reprinted with permission from ref 177. Copyright 2007 Optical Society of America. (b) Large 3D nanoparticle clusters as candidate ingredients for a metafluid. The extinction spectrum of the clusters is shown in the left panel, together with a scanning electron micrograph of a typical cluster. The magnetic permeability (μeff) and refractive index (neff) of a metamaterial generated from these clusters are shown in the middle and right panel, respectively. The real (red) and imaginary (blue) components are shown at two different volume fill factors (solid, ff = 0.5; dashed, ff = 0.1). Reprinted with permission from ref 181. Copyright 2013 American Chemical Society.

aggregated around dielectric cores.181 They measured the scattering spectrum of the metafluid, which showed the desired signature of optical magnetism and predicted that once sufficiently high volume fill factors of the clusters are achieved, negative magnetic permeability and negative refractive index would be obtained simultaneously at the same wavelength, as seen in Figure 12b.

are envisioned for them. The tetramer of the highly symmetric tetrahedral (Td) point group is of particular interest, as it was suggested by Urzhumov et al. as a candidate component for creating a metafluid, a medium simultaneously exhibiting negative permittivity and negative permeability.177 The anticipated optical properties of such a cluster are shown in Figure 12a, featuring optical excitation of the magnetic dipolar resonance. Alu and Engheta found that ring currents induced by the electric field of light in a symmetric plasmonic molecule of six nanoparticles of the D4h point group can lead to isotropic magnetic response at optical frequencies.178 As of today, these properties were not observed in natural materials, and plasmonic molecules provide a promising route to achieve them. Experimental efforts to generate 3D plasmonic molecules focused on methods for the self-assembly of higher-order nanoparticle clusters. Urban et al. used polymer encapsulation in order to obtain stochastically formed 3D clusters of 5−25 nanoparticles, among which they identified highly symmetric ones with an isotropic optical response, as expected for structures sustaining three-dimensional optically dark, magnetic modes.179 Yan et al.149 and Fan et al.180 fabricated substrate templates with voids of an appropriate size to trap a desired number of nanoparticles inside, which allowed them to obtain a series of 3D plasmonic molecules with 2 to ca. 10 nanoparticles. Dionne and co-workers used protein−antibody interactions to prepare a bulk metafluid composed of silver particles

2.5. Interference Effects in Plasmonic Spectral Lineshapes

It has been noted that scattering spectra of plasmonic molecules frequently possess asymmetric lineshapes.69,182,183 To understand such asymmetries, Hao et al. studied plasmonic molecules composed of a silver ring with a disk inside that was either co-centered or off-centered.184,185 Plasmon hybridization analysis showed that a symmetric arrangement of the individual dipole modes of the ring and disk components leads to an antibonding broadband bright mode. Interference between this super-radiant mode and the dark or subradiant mode of the plasmonic molecule, hybridized from the corresponding quadrupole modes of the ring and the disk, leads to an asymmetric line shape. The degree of asymmetry was found to be highly sensitive to the incident angle of the excitation light because the latter strongly affects the excitation of the quadrupole modes and consequently the phase of the scattered light.185,186 The plasmon hybridization formalism facilitated interpretation of the observed line shape asymmetry within an intuitive framework of coupled damped classical oscillators, only one of which can be driven by the applied force directly. 5552


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Figure 13. Interference effects in lineshapes of plasmonic molecules. (a) Scanning near-field optical microscope images of plasmon modes in heptameric plasmonic molecules with a Fano resonance. Amplitudes (|E|) and phases (φ) of the induced electric field are shown on the right (experimental and theoretical) for different detunings relative to the Fano dip in the extinction spectrum, as shown on the left. Reprinted with permission from ref 196. Copyright 2011 American Chemical Society. (c) Optical and photothermal spectroscopy of a plasmonic oligomer: (top panel) scanning electron microscope image; (middle panel) scattering (red line) and absorption (green line) spectra of the cluster, a Fano resonance appears only in the scattering spectrum; (bottom panel) charge distributions calculated at the spectral positions marked 1 and 2 in the middle panel. Reprinted with permission from ref 205. Copyright 2016 American Chemical Society.

The corresponding asymmetric line shape could be understood as a classical version of the Fano resonance.182,183,187,188 Mukherjee et al. extended these results, obtained for planar plasmonic molecules, to the three-dimensional counterparts of the ring-disk plasmonic molecules, spherical off-centered nanoshells.189 Further to single composite nanoparticles and dimers, the Fano resonance effect was extensively studied in plasmonic molecules of multiple different configurations, including symmetrical and symmetry-broken arrangements of tetramers, pentamers, hexamers, and larger oligomers.144,159,162,190−194 Multiple Fano resonances were observed in the latter case, corresponding to different dark modes of the plasmonic molecule.195 Hillenbrand and co-workers used near-field optical scattering microscopy to map the spatial field distribution of Fano modes in plasmonic molecules.196 A remarkable agreement between their real-space amplitude and phase imaging and a numerical calculation of the Fano lineshapes was obtained, as seen in Figure 13a. Link and co-workers used

photothermal spectroscopy to study absorption in individual plasmonic molecules possessing Fano resonances and found that, in contrast to the spectrum of scattered light, the absorption spectrum does not carry a dispersive dip (Figure 13b).197 They thus confirmed the theoretical finding that the observed Fano lineshapes are essentially an outcome of the interference between light scattered by the optically bright and dark plasmon modes, coupled via the near-field. Consequently, the appearance of the Fano dip depends on the relative orientation of the polarization of excitation light with respect to the principal axes of the plasmonic molecule. Chang et al. used this idea to realize switching of a Fano line shape on and off in a plasmonic molecule embedded within a nematic liquid crystal, using an applied voltage to rotate the polarization of the incident light.198 Because subradiant modes involved in the Fano resonance phenomenon have low radiative loss as compared to superradiant modes, their plasmon-enhanced near-field can be advantageous for surface-enhanced spectroscopy.199 Immediate 5553


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Figure 14. Quantum effects in plasmonic molecules. (a) EELS spectroscopy of small nanoparticles showing quantum size effects. The spectrum blueshifts as the particles become smaller, an effect that requires quantum theory to explain. Electron microscopy images of the particles are shown to the right of the spectra. Reprinted with permission from ref 219. Copyright 2012 Nature Publishing Group. (b,c) A thin organic layer of benzenedithiol (BDT), separating two silver nanocubes (b), facilitates electron tunneling between them, seen in EELS spectra as a new resonance at low energy, known as a charge-transfer mode. A layer of ethanedithiol (EDT) does not show the same effect. Reprinted with permission from ref 220. Copyright 2014 American Association for the Advancement of Science.

coupled oscillator model to incorporate radiative interactions.210 Another mechanism for Fano lineshapes in plasmonic systems, based on the formalism of nonorthogonal eigenmodes (a concept used in non-Hermitian quantum mechanics),211 was proposed by Kivshar and co-workers.153,212 Their work facilitated the extension of the plasmonic molecule paradigm also to dielectric materials. Interference effects in plasmonic molecules are not limited to line shape asymmetries. An interesting aspect of coupling between bright and dark modes in plasmonic molecules was demonstrated by Taubert et al.,213 who found that changing the relative location of the components in a nanofabricated 3D plasmonic molecule induces a phase shift in their coupling, which may lead to enhanced absorption. The authors viewed this as a classical analogue of electromagnetically induced absorption. Another consequence of interference in light scattering by plasmonic molecules was employed by Shegai et al., who constructed a directional color routing device based on a heterodimer composed of nanoparticles of two different metals.214,215 Because of the large detuning between the individual resonances of the nanoparticles, the two longitudinal dipolar modes of the plasmonic molecule are hybridized only to a small extent and both appear to be bright. Controlling the interference between the light scattered by these normal modes by tuning their relative phase via the interparticle distance leads to a situation where the direction of the scattered light depends on its wavelength. The dependence of the light scattering direction on such interference in heterodimers was further used to contruct a sensor for hydrogen based on modulation of the permittivity of palladium upon hydrogen binding.215

and pertinent examples include refractive index sensing by linear spectroscopy175 and SERS.200 In addition, coupling to the dark mode was used to enhance nonlinear interactions,201−203 ultimately leading to a realization of surfaceenhanced coherent anti-Stokes spectroscopy of single molecules.204 As already discussed, EELS is an efficient method to study optically dark modes of plasmonic molecules. As distinguished from the optical plane-wave excitation, in EELS the excitation is localized and the “selection rules” for plasmon modes depend on the position of the electron impact.67,122,131,206 Theoretical modeling of a heterodimer of nanorods suggested that Fanolike interference effects would be observed also in EELS and cathodoluminescence spectra, with the nature of the interference (constructive or destructive) depending on the excitation position.207 Some experimental validation of this promising idea of spatial control over the near-field was obtained.208 So far, we have discussed Fano lineshapes emanating from near-field coupling between an optically dark plasmon mode and a bright plasmon mode. Different mechanisms leading to this effect were also put forward. Forestiere et al. showed that Fano lineshapes could be induced by the destructive interference of the light scattered by two or more bright modes uniformly excited by a plane wave.209 They derived analytical expressions in the quasi-static regime for calculations of the Fano resonance and elucidated the mechanism of such an interference in the scattering spectrum and its absence in the absorption spectrum. The role of radiation damping in the formation of a Fano line shape by interference between bright modes was demonstrated by Lovera et al., who extended the 5554


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predictions of classical theory.226 In addition, they found that in the quantum tunneling regime, the low-energy bright plasmon mode blue-shifts as the interparticle distance is decreased, as opposed to the red-shift seen in the classical regime. To reduce the computational costs of the application of quantum theory to modeling plasmonic molecules, Esteban et al.227 developed a so-called quantum-corrected model, where the quantum mechanical effects (electron tunneling and tunneling resistivity) are incorporated locally into the dielectric function of the material in the interparticle gap. The charge transfer mode, associated with interparticle quantum tunneling of the conduction electrons, is a natural characteristic of the quantum regime.228−232 The onset of quantum tunneling may depend on the material in the gap between the particle. Indeed, while experiments by Duan et al.133 on nanofabricated bowties with gaps down to 0.5 nm showed classical electromagnetic behavior, experimental results of Reinhard and co-workers on DNA-tethered silver nanoparticle dimers with gaps larger than 1 nm indicated quantum tunneling.233 The resolution of the apparent contradiction between these two reports may be the ability of the DNA molecules in the latter experiment to sustain electron tunneling between the particles. More recently, Lerch and Reinhard suggested a molecule-mediated quantum tunneling charge transfer process to explain experimental optical spectra of DNA-tethered dimers with gaps as large as 2.8 nm.234 Interestingly, molecule-mediated charge transfer between plasmonic particles was already discussed in early SERS literature, as summarized by Brus and co-workers.235 Additional experimental evidence for the role of quantum tunneling was presented by Scholl et al., who used the STEM method of Batson et al.48 (already mentioned in section 2.2) to create dimers with very small gaps.236 They then performed EELS spectroscopy and detected clear signatures of the charge transfer mode. The experimental EELS measurements of Tan et al.220 again demonstrated how molecules can increase significantly the interparticle distances over which a chargetransfer plasmon mode is observed. The charge-transfer resonance they measured was facilitated by a layer of benzendithiolate molecules but not by ethanedithiolate molecules (Figure 14b,c). The above results were recently questioned in a theoretical study by Knebl et al.,237 who did not observe a charge transfer mode in their calculations. Further discussion on using molecules to study plasmonic near-fields in the quantum limit can be found in Section 3.1. The development of theoretical methods for accurate description of plasmon fields in the quantum regime is the subject of continued work in the field.238−241 Recent studies indicated that, in addition to the material properties, quantum tunneling effects can strongly depend on the geometry of the nanoparticle cluster via the identity and symmetry of the corresponding plasmon modes involved. For example, Marinica et al. predicted that light-induced current across the interparticle gap of nanoparticle dimers can lead to a strong nonlinear response.242 On the other hand, Dionne and coworkers showed both in experiment and simulation that plasmon modes that do not involve enhanced fields within interparticle gaps (dark modes) are not affected by quantum interactions even at the smallest gap sizes.243

2.6. Quantum Effects in Plasmonic Molecules

The characteristic dimensions of a plasmonic molecule are either the sizes of the nanoparticles composing the molecule or the interparticle distances. As these characteristic dimensions become smaller, the optical properties of plasmonic molecules deviate from the theoretical description based on classical electrodynamics. In this regime, quantum mechanical theory should be used to describe experimental observations. In this section, we discuss cases where the transition from classical to quantum description should be made. In small nanoparticles, down to a size of only few nanometers, lineshapes broader than expected based on classical electromagnetic theory were observed.216,217 Because the ratio of surface area to volume increases in smaller nanoparticles, modification of the bulk dielectric function with a term accounting for the effect of electron-surface scattering was suggested to explain results of ensemble measurements.216 A correction to the dielectric function was also used to rationalize observations of lineshape broadening in single-nanoparticle spectroscopic experiments.218 Recently, in an EELS study, Dionne and co-workers have found that surface plasmon resonance frequencies in nanoparticles as small as only a few nanometers cannot be explained by such a correction, which would predict a slight red-shift of the plasmon resonance with reduction of the nanoparticle size. Instead, they found that the plasmon resonance blue-shifts significantly,219 as seen in Figure 14a. A quantum description of the conduction electrons moving within the nuclear potential was used to understand these results. Because a full quantum-mechanical description of plasmonic structures with realistic dimensions is highly computationally demanding, alternative theoretical approaches have been developed. A nonlocal semiclassical electromagnetic theory was introduced by Garcia de Abajo221 and extended by McMahon et al.222,223 and further by Mortensen et al.224 This approach is based on the assumption that the dielectric function of the material depends both on the frequency and the wave vector. The electromagnetic theory modified to account for the nonlocal response through the dielectric function was found valid for nanoparticles consisting of thousands of metal atoms and of sizes exceeding the Fermi wavelength. In the case of plasmonic molecules, classical electromagnetic theory predicts stronger near-fields for smaller interparticle gaps due to an increasing admixture of higher-order multipoles. However, Hao and Schatz noted already in 2004, that at interparticle distances below several nanometers classical electrodynamics may fail to predict the electromagnetic fields around nanoparticle dimers and the corresponding plasmon spectrum.103 Garcia de Abajo and co-workers demonstrated that accounting for nonlocal effects can overcome the failure of the standard theory and should allow for evaluation of the electric fields around dimers of nearly touching nanoparticles, as seen in Figure 14b.221,225 When the interparticle distance is smaller than 1 nm, a purely quantum effect involving electron tunneling across the gap becomes important. Electron tunneling cannot be captured by the nonlocal dielectric function, and a full quantum description is required to capture its effect on both near-field enhancement and plasmon spectrum. Zuloaga et al. studied quantitatively the enhancement of the near-field in nanoparticle dimers with decreasing gaps, using time-dependent density functional theory, and found that for interparticle distances below 1 nm, quantum effects significantly reduce the enhancement as compared to the

2.7. Chirality Effects in Plasmonic Molecules

Many important chemical properties of molecules are linked to the chiral centers found in their functional groups, as for 5555


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Figure 15. Chiral plasmonic molecules. (a) Transmission electron micrographs of plasmonic nanoparticles assembled in chiral structures with DNA templates of right and left handedness (scale bar, 20 nm) and their corresponding CD spectra. Reprinted with permission from ref 51. Copyright 2012 Nature Publishing Group. (b) Chiral plasmonic oligomers fabricated by electron beam lithography (scale bar, 200 nm) and their differential circular light polarization transmission spectra. Scanning electron micrographs of the right- and left-handed structures are shown on the right, and their corresponding spectra are shown on the left in red and blue, respectively. The spectrum of the achiral control structure is shown in black. Reprinted with permission from ref 253. Copyright 2012 American Chemical Society. (c) Experimental demonstration of plasmon-induced CD in chiral molecules adsorbed on plasmonic atoms. Adsorption of riboflavin on gold islands induces a new CD band at 575 nm (blue line). Reprinted with permission from ref 260. Copyright 2013 American Chemical Society. (d) Theoretical calculations of plasmon-induced CD spectra of an individual chiral molecule (top panel) (CD response at 290 nm), and a chiral molecule interacting with a plasmonic nanoparticle (middle and bottom panels) for different orientations of the molecular electric and magnetic dipoles with respect to the nanoparticle surface, showing a plasmoninduced CD signal in the visible range (525 nm). Reprinted with permission from ref 261. Copyright 2010 American Chemical Society.

nanoparticle or by the microscopic topographical properties of its surface and its geometric shape.246 Recently, Valev et al. reviewed linear and nonlinear optical properties of planar (2D) and three-dimensional (3D) chiral nanostructures, focusing on their role as metamaterials.247 Hentschel et al.,248 and Ma et al.,249 summarized experimental approaches for the fabrication of chiral nanostructures using both top-down and bottom-up strategies and their promising application for chiral sensing. In the classification scheme suggested by Ben-Moshe et al.,250 the vast amount of recent literature on chiral plasmonics can be divided into the following categories: (a) plasmonic atoms of chiral shapes, (b) chiral plasmonic molecules made from achiral plasmonic atoms, (c) plasmonic molecules made of chiral

example in amino acids, or to the overall helicity of their secondary structure, as in peptides or DNA strands. Spectroscopic manifestations of chirality, namely optical rotatory dispersion (ORD) and circular dichroism (CD), are extensively used for molecular characterization. Plasmonic molecules possessing such chiroptical effects were extensively studied in the past decade, inspired by structural motifs of chiral molecules. Interestingly, optical activity of a perfect metallic sphere can be brought about by the generation of spiral currents on its surface, as was predicted by Bohren, who extended Mie theory to account for this case.244,245 A more common and experimentally relevant scenario involves optical activity caused by chiral ligand molecules on the surface of a 5556


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Figure 16. Single-molecule SERS. (a) Time-resolved SERS spectra of a single R6G molecule recorded at 1 s intervals. Note abrupt changes in intensity and frequency of some of the lines. Reprinted with permission from ref 265. Copyright 1997 American Association for the Advancement of Science. (b) Enhancement factor distribution in the region of the gap (2 nm) between two gold colloids (radii = 30 nm) calculated in the electrostatic approximation with finite-element modeling. Reprinted with permission from ref 275. Copyright 2008 Royal Society of Chemistry. (c) Time-dependent spectral trajectory of a single R6G molecule, showing strong spectral fluctuations. Each row contains one color-coded spectrum. Reprinted with permission from ref 271. Copyright 2001 American Chemical Society.

phase delay.257 The experimental application of this model to 3D plasmonic molecules of nanorods demonstrated its validity for both CD and ORD measurements.258 Hentschel et al. used the plasmon hybridization framework to understand the role of plasmon energetics in CD spectra.259 By modifying the nanostructure geometry, they were able to show that inversion of relative energies of the participating plasmon modes leads to inversion of the CD spectral shape, as expected for mirrorsymmetric structures, enantiomers. Maoz et al. demonstrated experimentally that plasmon resonances of nonchiral nanoparticles can be used for sensing chiral molecules (case (d) above, see Figure 15c).260 The chiral response of a molecule is a result of the interaction of light with its electric quadrupole and magnetic dipole moments. When molecular and plasmon resonances overlap, the enhanced nearfield around the nanoparticles can strongly amplify the otherwise weak CD response of the molecule. However, the corresponding molecular resonances typically appear in the UV or in the blue part of the visible spectral range, whereas the plasmon resonances are in the visible region. Interestingly, when molecules were placed in the vicinity of plasmon nanoparticles, the chiral response was observed also in the visible region, around the plasmon resonance.260 It is important to realize that while the CD signal due to the molecular response rapidly vanishes outside the molecular transition region, ORD decays much more slowly with frequency. This

plasmonic atoms, and (d) achiral plasmonic molecules (or atoms) interacting with chiral molecules. The origin of optical activity in cases (a,b) above is probably the more intuitive of all cases, as the analogy to the familiar molecular cases can be readily drawn. Govorov and co-workers derived a classical electromagnetic analogue to the quantummechanical theory of CD for chiral plasmonic molecules made of small nanoparticles.251 They showed that the optical activity is caused by interparticle Coulomb interaction and is sensitive to the geometry and composition of the plasmonic assemblies. Within this mechanism of plasmonic CD, large interparticle distances and, therefore, weak interactions, are assumed. However, one can still describe such plasmonic molecules in terms of their corresponding normal modes. Thus, the differential absorption of circularly polarized light with different handedness is due to the different excitation cross sections of the corresponding collective dipolar modes with chiral nature. Several experimental realizations of the above ideas were reported (Figure 15a,b).51,252−255 Plasmonic molecules with smaller interparticle distances, where multipole effects arise, were also studied.256 A complementary theoretical concept was introduced by Yin et al.,257 who developed a classical model of optical activity in plasmonic molecules based on orthogonal coupled mechanical oscillators displaced in the direction of light propagation. These oscillators are driven by the electric field of light with a relative 5557


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Figure 17. Super-resolution imaging of SERS hotspots. (a) A hotspot formed on silver nanoclusters probed with fluorescent molecules. Note the small dimensions. Reprinted with permission from ref 292. Copyright 2011 Nature Publishing Group. (b) Two-dimensional SERS intensity distributions within individual hotspots on silver clusters, indicating molecular diffusion. Reprinted with permission from ref 293. Copyright 2010 American Chemical Society. (c) Correlation of a SERS intensity map (left upper panel) and scanning electron micrographs (right upper panel) demonstrates that the hotspot is in the gap between particles (lower panel). Reprinted with permission from ref 294. Copyright 2011 American Chemical Society.

forefront of our understanding of plasmonic enhancement. Perhaps initiating this trend were Xu et al.,29 who used electromagnetic theory to calculate the enhancement of Raman scattering in different configurations of plasmonic molecules and found that the highest enhancement is obtained in the junction of a dimer whose particles that are separated by just 1 nm. The notion of the gap enhancement, or “hot spot” has become popular when it was shown that the Raman signal from a single molecule has a uniaxial symmetry, matching the expectation for two adjacent particles. 24,267 In current terminology, we may state that the observed enhancement was due to excitation of the bright dipolar mode of the particles (see section 2.2). The study of SERS from single molecules or a small number of molecules has become a fruitful of research, driving multiple applications in sensing and detection of molecules. This field has been summarized in multiple reviews (see, e.g., 27,268). Our interest here is limited to the intimate relation between SERS and the gaps of plasmonic molecules and the ability to use SERS to monitor the electromagnetic fields within these gaps.

difference in the spectral response is the basis of the theoretical description developed by Govorov and co-workers (Figure 15d), who identified the origin of this effect as the dissipation of the off-resonant molecular excitation in the form of a chiral current on the metal nanoparticle, which is stronger at frequencies close to the plasmon resonance.261−263 They also showed that plasmonic hot spots can greatly enhance the corresponding signals.264

3. INTERACTION BETWEEN PLASMONIC MOLECULES AND THEIR NEIGHBORS 3.1. Surface-Enhanced Raman Spectroscopy As a Probe of Plasmonic Fields

That local surface plasmon fields can enhance the spectroscopic signals of molecules adsorbed near the surface has been known for many years.12 The discovery of single-molecule Raman spectroscopy in 1997265,266 has led to increasing interest in the potential of plasmonic structures as amplifiers for weak molecular signals. Soon after this discovery, the importance of the interparticle gap13 returned with full force to the 5558


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Figure 18. Probing electromagnetic fields in the gaps of DNA-based nanoparticle dimers. (a) Dimers were constructed using DNA hybridization, and a SERS probe was positioned in the middle of the construct. Reprinted with permission from ref 301. Copyright 2009 Nature Publishing Group. (b) AFM images of DNA-based dimers with varying gap sizes. Reprinted with permission from ref 300. Copyright 2012 American Chemical Society. (c) SERS spectra of individual Cy3 molecules within the gaps of the dimers in b. The SERS intensity decreases as the gap size increases, tracing changes in the strength of the electromagnetic field in the gap. Reprinted with permission from ref 300. Copyright 2012 American Chemical Society.

The Raman scattering process involves two different frequencies, namely the excitation frequency and the scattering frequency; the latter is lower than the former in the case of Stokes scattering or higher than the former in the case of antiStokes scattering.269 The plasmon-enhanced Raman signal can therefore be written as involving two electromagnetic field interactions with the particles.12,270 First, the excitation field is enhanced near the surface of the particles, creating a local field that is significantly stronger than the external one. Second, the field scattered by molecules (at a shifted frequency) is enhanced by the particles and rescattered to the far field. Both factors require excitation of plasmonic modes, each at its own frequency. The overall enhancement is a product of the two enhancement steps. What is the maximum enhancement attainable in the gaps of plasmonic molecules? Early experimental work reported enhancement factors as high as 14 and even 15 orders of magnitude. This stood in contrast to the calculations of Xu et al.,29 which showed significantly smaller enhancement factors. Some of this confusion arose from the fact that rhodamine 6G (R6G) was extensively used as a probe molecule in the early single-molecule SERS studies25,265,271 (Figure 16a). The molecular resonance effect of R6G was therefore at play in addition to the plasmonic enhancement. Together these two effects led to an enhancement of ∼14 orders of magnitude. Later on, it was realized that the resonance Raman contribution is particularly strong in R6G, providing some 6 orders of magnitude of enhancement.272 Further, careful analysis of the plasmonic enhancement within the gap between two particles by Xu et al.29 and Le Ru et al.273 showed that the maximum attainable enhancement is ∼10−11 orders of magnitude. Le Ru et al.273 also showed that an enhancement of 107 is enough for the detection of Raman scattering from a single molecule. In a separate work, these authors also provided a thorough theoretical description of hot spots and the distribution of the EM field within and around them (Figure 16b).274,275

Following the initial realization that Raman scattering can be observed from single molecules,265,266 it was noted that the signals show some interesting and unexpected characteristics. Indeed, single-molecule spectra were shown to fluctuate, both in their overall intensities and in their shape28,265,267,271,276−289 (Figure 16c). It took some time for an authoritative approach to be developed for proving that the single-molecule level has been attained. Indeed, it was Etchegoin and Le Ru who first proposed such a technique, the bianalyte method, in which two different molecules are sampled together. In the singlemolecule limit, the gap of a plasmonic molecule would contain only one of the two molecular species, and therefore only pure single-species spectra should be observed.290 Van Duyne and co-workers improved this method by using isotopologues of the same molecule rather than two different molecules.291 New imaging tools such as super-resolution microscopy allowed scientists to probe in greater detail the motion of individual molecules into and around the gaps of plasmonic molecules292 (Figure 17a). Willets and co-workers championed the use of SERS for this purpose.293 They mapped the position of SERS signals of single molecules with a 10 nm spatial resolution and demonstrated that the molecules move over regions that are larger than the expected sizes of hot spots (Figure 17b). By combining their localization results with scanning electron microscopy images, they were able to correlate the molecular distribution with the structure of the particles and obtain novel information on the SERS hot spots.294 Interestingly, probed molecules were found to be clearly confined to a single interparticle gap within a plasmonic cluster (Figure 17c). These experiments clearly indicated that at least part of the reported intensity fluctuations can be attributed to sampling of the electromagnetic fields in the plasmonic molecule gaps by the diffusing molecules. However, there is some evidence that part of the spectral fluctuations are due to variations in charge transfer interactions between the molecules and the metallic surfaces.271,285,287 The role of charge transfer interactions in SERS has been debated for many years,19,295,296 yet their 5559


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Figure 19. Probing the approach of the quantum regime with SERS. (a,c) A nanofabricated plasmonic dimer with an atomic length-scale gap size probed with a transmission electron microscope. (b) SERS enhancement factors from a series of nanofabricated dimers with varying gap sizes. At the smallest gap sizes, the SERS enhancement decreases, a manifestation of the quantum regime. Reprinted with permission from ref 302. Copyright 2014 Nature Publishing House.

molecular resonance enhancement, as discussed above. The SERS signal became weaker as the gap size was increased. It is important to realize that this inverse relation between gap size and enhancement is complex because it involves not only an overall reduction of the plasmonic field in the gap but also a shift of the plasmon spectrum due to a reduction in the coupling between particles. This complex behavior defies a simple analytical description of the gap-size dependence of the enhancement. Most significantly, the intensity of the SERS signal measured from individual molecules by Suh and colleagues300 also decreased when the gap was almost closed, suggesting the approach of the quantum regime (see section 2.7 for a detailed discussion of quantum effects in ultranarrow interparticle gaps). A systematic probe of the quantum regime using SERS was performed by Zhu and Crozier.302 They used electron beam lithography to generate plasmonic dimers made of 90 nm gold discs. The gaps between the discs were varied down to the Ångstrom size, and measured accurately for each dimer from electron micrographs. A thiophenol monolayer was deposited on top of the discs, and its Raman signal was registered. The Raman enhancement was found to increase monotonically as the gap size decreased from 10 nm to ∼7 Å (Figure 19). Below this gap size the enhancement decreased, signifying very clearly the appearance of the quantum regime. The trend seen in the experiment could be roughly matched by calculations based on a quantum-corrected model.239 Two particularly advanced methods devised to systematically vary the gap size in plasmonic molecules, based on the use of DNA strands and on nanofabrication techniques, were discussed above. A third method employed by several groups involved covering particles with oxide layers of well-defined thickness. Such layers can be formed on gold303,304 or silver305 particles and can even be used to create plasmonic molecules by encapsulating two or more particles.306 Oxide layers can also be formed on gold surfaces (mirrors).307,308 Adsorption of

involvement in the induction of chemical reactions on plasmonic molecules is of much current interest (see section 3.3). Early experiments relied on aggregation of metallic particles, either spontaneous or induced by the addition of salt or other chemicals. When it was realized that SERS signals can be used to probe the properties of plasmonic gaps, attempts were initiated to engineer hot spots in a systematic fashion. For example, a bifunctional molecule was used as a means to connect two silver particles together to form a plasmonic dimer.30 The same molecule was used to probe the gap by scattering Raman photons. It was found that when larger particles were used, which increased the interparticle coupling, the shape of the Raman spectrum of the molecule also changed, thus reporting on changes in the near-field plasmonic spectrum. Dimers could also be produced by using proteins or a combination of DNA and proteins to couple particles297,298 or by using advanced fabrication methods such as on-wire lithography.299 A much more sophisticated method to generate metal particle dimers, which facilitated control over the gap size, was described by Suh and co-workers300,301 (Figure 18). The goal of these authors was to generate plasmonic dimers with a welldefined gap size and exactly one molecule in the gap, to be probed by SERS. Gold nanoparticles were modified with DNA sequences that were then hybridized together to form dimers. The gaps were narrowed down by depositing silver shells on the particles. A series of constructs with varying particle diameters and gap sizes was prepared in this way, with the interparticle gaps varying from 5 nm down to ca. 0.5 nm.300 In these experiments, the interaction between the plasmon modes of the nanoparticles was manifested through the SERS signal enhancement. This enhancement was found to be maximal for dimers made of 50 nm particles with sub-1 nm gaps, with a reported average enhancement factor as high as ∼2 × 1013, due to a combination of the plasmonic enhancement with the 5560


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Figure 20. Plasmonic dimers created by placing nanoparticles on a mirror. (a,b) Scheme of a system of nanoparticles separated from a gold surface (mirror) by self-assembled monolayers and a confocal SERS scan of the area of such a sample. The nanoparticles appear as intense spots. Reprinted with permission from ref 309. Copyright 2008 Wiley. (c) Scheme of particles separated from a mirror by an oxide layer. (d) High-resolution TEM image of one particle separated by a 2 nm silicon oxide spacer from the mirror. (e) SERS intensity from thionine molecules deposited on structures such as in panel d, as a function of the spacer thickness. (c−e) Reprinted with permission from ref 307. Copyright 2012 American Chemical Society.

spectrum, and their fields interfere with each other, the far-field response may vary across the spectrum. The polarization of the measured Raman spectrum was found to accurately report on this phenomenon. Thus, for example, in some plasmonic trimers, the interference of the two dipolar modes could convert the linear polarization of the excitation light into circular polarization in the Raman-scattered light (Figure 21a,b). A similar effect may also lead to a strong circular dichroism response in the spectrum of molecules on a trimer (Figure 21c).310 In this section, we demonstrated that SERS can be used to probe the fields in the gaps of plasmonic molecules. As discussed in previous sections, various methods have been employed to probe the fields around plasmonic molecules and within their gaps, including near-field microscopy and EELS. It would be interesting to compare information obtained by one of these techniques to SERS. That was the focus of a recent paper by Camden and co-workers, who performed SERS and EELS experiments on the very same plasmonic molecules.311 They found that in plasmonic molecules that support singlemolecule SERS, the EELS signals within the gaps were consistently weak. This was attributed to the fact that the electron beam could not couple to the bonding mode, which is the dominant mode within the gaps, and is therefore responsible for the strong Raman enhancement. However, the bonding mode could be excited when the beam was placed

particles on such surfaces (or on monolayers of molecules that are self-assembled on top of them, see ref 309) creates plasmonic molecules that are sometimes called “nanoparticles on a mirror” (NPOM, Figure 20). In this case, the coupling can be thought of as occurring between an adsorbed particle and its image in the mirror. The gap size dependence of SERS signals was also probed with such constructs in the above publications, although the quantum regime (below 1 nm) could not be reached. The calculation of the enhancement factor in these systems must take into account the refractive index of the intervening oxide layer, posing significant challenges for the accurate reproduction of experimental results.307 SERS has been found useful in probing plasmonic molecules with more than two particles. Such plasmonic molecules have additional attributes to the particle size and interparticle gap size that characterize plasmonic dimers. In particular, the geometric arrangement of the particles determines both the number of gaps as well as the symmetry, which in turn dictates their plasmonic normal modes, as discussed in section 2.5. Because, as discussed above, the Raman scattering of a molecule situated on a plasmonic molecule is enhanced by the interaction with the particles, it becomes interesting to find out which normal modes of the cluster are excited. Chuntonov and Haran showed that in general in a trimeric plasmonic molecule two orthogonal in-plane dipolar modes are excited by the light scattered from a molecule in one of the interparticle gaps.148 Since each of these two modes may have its own 5561


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starts the chemical process. The role of hot electron transfer from particles to molecules has in fact been discussed for many years and is the basis for the so-called chemical enhancement or charge transfer mechanism of SERS.19,295 More recently, the role of plasmon-generated hot electrons in various physical and chemical process has garnered new interest (Figure 22a).315−317 A popular reaction for studying plasmon-enhanced chemistry has been the photoconversion of 4-nitrobenzenethiol (NBT) through the intermediate 4,4′-dimercaptoazobenzene (DMAB) into the stable product 4-aminobenzenethiol (ABT).318−321 In the context of the current review, we are particularly interested in chemical reactions that were enhanced within the gaps of well-defined plasmonic molecules. Xie et al.322 generated rather complex plasmonic molecules made of a single core gold particle of 80 nm to which small gold particles were attached. The particles were immersed in an NBT solution, and sodium borohydride was added to initiate the reaction, which was followed with SERS. More recently, they were able to show that the reaction can occur in the absence of the reducing agent and proposed a mechanism involving hot electrons (Figure 22b).323 Zhang et al.324 studied the NBT reaction on isolated gold dimers. They used three dilutions of the molecule and followed its fate using SERS. At 10−7 and 10−8 M and under a high enough laser flux, they could trace the formation of DMAB from NBT, attributing it to a plasmon-induced hot-electron effect. At 10−9 M, they no longer saw the formation of DMAB, likely because the NBT molecules were already too far from each other to react. Instead, they saw indication for a unimolecular reaction, namely the formation of thiophenol. Most recently, Kim and co-workers used NPOMs to study chemistry down to the level of the single molecule (Figure 22c).325 As it turned out, the application of NPOMs facilitated studying the reaction at the limit of individual chemical events. Indeed, SERS spectra taken as a function of time showed steps in the intensities of spectral peaks, particularly those attributed to DMAB. These steps were assigned to individual events of formation or annihilation of a DMAB molecule. The authors were able to characterize the kinetics of the reaction in detail based on the statistics of steps and to show branching between two different reaction paths. This study thus brought plasmoncatalyzed chemistry to the bona fide single-molecule level for the first time. It will be interesting to see how this field develops in the coming years and in particular whether additional classes of reactions are shown to be catalyzed by hot electrons on welldefined plasmonic molecules and at the single-molecule level.

Figure 21. Plasmonic trimers affect the polarization properties of the far-fields of molecules. (a) Scanning electron micrograph of a trimer of silver particles. (b) Polar plot of the polarization response of the trimer in a, measured at two different wavelength. At 555 nm (black dots), the polarization is almost linear, while at 583 nm, the polarization is circular due to interference between two plasmonic modes. Reprinted with permission from ref 148. Copyright 2013 American Chemical Society. (c) A similar effect can lead to a strong circular dichroism in the spectrum of molecules on trimers. The main response is due to an electric dipole−electric quadrupole combination (ED−QD), as opposed to the more standard electric dipole−magnetic dipole combination (ED−MD). Reprinted with permission from ref 310. Copyright 2017 Royal Society of Chemistry.

3.3. Surface-Enhanced Fluorescence, Infrared Absorption, and Nonlinear Optical Signals

While Raman enhancement is quite a spectacular phenomenon, facilitating observation down to the single-molecule level, it is also possible to enhance other spectroscopic signals. The enhancement of molecular emission has attracted much attention, as it paves the way to stronger fluorescence signals with reduced photobleaching, which might be useful in multiple applications. Fluorescence is enhanced because of two factors. First, the enhanced electromagnetic fields at the gaps between nanoparticles lead to enhanced excitation of the molecules placed there. This is similar to the first enhancement step in SERS. Second, the plasmonic molecule acts as a resonant cavity to enhance the radiative rate of a quantum emitter, due to the increased local density of states.326 Because the competition between radiative and nonradiative channels determines the emission rate, an enhancement of the radiative rate is translated

outside the gap. A similar finding was reported by Kadkhodazadeh et al.312 3.2. Surface-Enhanced Raman Spectroscopy As a Probe of Chemical Reactions

Many years ago, Nitzan and Brus suggested that photochemical reactions might be enhanced at rough surfaces.313 While some validation of this idea had appeared over the years,314 the discovery of ultrastrong surface enhancement in recent years and the appearance of well-designed SERS hot spots in plasmonic molecuels have injected new excitation into this field of research. There is now some consensus that chemical reactions may be driven by the injection of a hot electron from the plasmonic system into an adsorbed molecule, which then 5562


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Figure 22. Chemistry within the gaps of plasmonic molecules. (a) Two possible routes of charge transfer into an adsorbate: (left) indirect mechanism whereby plasmon relaxation generates hot electrons that can tunnel into the adsorbate; (right) decay of a resonant plasmon causes an electron to transfer directly into an unoccupied adsorbate state. Reprinted with permission from ref 317. Copyright 2015 Nature Publishing House. (b) Photoconversion of NBT into ABT on plasmonic molecules. Bands due to the product are marked with a dashed red line. Reprinted with permission from ref 323. Copyright 2015 Nature Publishing House. (c) Discrete steps in the SERS trajectory of DMAB, indicating formation and disappearance of DMAB molecules one by one. Reprinted with permission from ref 325. Copyright 2015 American Chemical Society.

enhancement could also be achieved with individual gold nanorods.332 Recent experiments focused on optimizing the synthesis of plasmonic dimers with a well-defined gap size in order to obtain strong fluorescence enhancement. Thus, for example, Tinnefeld and co-workers used DNA origami to position gold nanoparticle pairs at a gap of 12−17 nm and obtained very large enhancement factors333 (Figure 23c), while Wenger and co-workers developed a sophisticated nanofabrication methods that allowed them to generate pairs of particles with gap sizes down to 10 nm, also showing impressive enhancement of the fluorescence signal from molecules swimming through the gap (Figure 23d).334 These authors reported fluorescence enhancement of 15000 for fluorophores with a low quantum yield. In addition to fluorescence of molecules situated within the gaps of plasmonic molecules, it is also interesting to observe the self-photoluminescence (PL) signal of metals, which is the outcome of excitation of electrons from the d-band into the conduction band and their eventual return to the d-band. This PL can be excited with single photons or with two photons.335 Moerner and co-workers demonstrated enhancement of twophoton PL from gold bowtie structures, which increased as the gaps within these plasmonic molecules decreased.336 The gap dependence matched the expectation based on the local plasmonic fields at the gaps. Another important spectroscopic signal that can be enhanced by plasmonic structures is infrared absorption, which can provide complementary information to Raman scattering. Surface-enhanced infrared absorption (SEIRA) has developed significantly in recent years and has found valuable applications. A recent review by Neubrech et al.337 in this journal summarizes the state of the art of this field, and therefore we

into enhanced emission. The enhancement of the emission of a quantum emitter placed within a plasmonic molecule, E, can be written as follows:327 E=

γex γr γex0 γr0

1 q0(γr + γET)/γr0 + 1 − q0

(1)

where γ0ex, γ0r , and q0 are the excitation rate, radiative rate, and quantum efficiency of the quantum emitter, respectively, γex and γr are the enhanced excitation and radiative rates in the presence of the plasmonic molecule, respectively, and γET is the rate of nonradiative energy transfer from the emitter to the plasmonic molecule. If q0 is close to 1, the enhancement due to the increase of the radiative rate is minimal and might even be offset by the nonradiative energy transfer. On the other hand, if q0 is small, there is additional enhancement due to the increase in the radiative rate. Novotny and co-workers showed early on that the ideas embodied in eq 1 can be demonstrated in the lab.327,328 They approached individual dye molecules situated on a surface with single gold and silver particles and registered the photon flux emitted by each molecule upon excitation with a laser. Good agreement with eq 1 was achieved. A similar result was obtained soon afterward by Sandoghdar and co-workers.329 The overall fluorescence enhancement in these experiments was rather modest. A much stronger enhancement could be registered in the gaps of plasmonic dimers, with E > 1000 for some individual molecules (Figure 23a).330,331 It was also shown that dimers can be used to shape the emission spectrum of fluorescent molecules:298 as the distance between two gold particles was decreased, the plasmon spectrum shifted to the red, and so did the fluorescence spectrum of molecules situated within the gap (Figure 23b). Interestingly, strong fluorescence 5563


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Figure 23. Surface-enhanced fluorescence in plasmonic dimers. (a) A bowtie antenna can concentrate the electromagnetic field in its gap: (top panel) electron micrograph showing the structure of a bowtie, (middle panel) calculation of electromagnetic field around the structure, showing the strong enhancement in the gap. The bottom panel shows the fluorescence enhancement in bowties as a function of gap size. Reproduced with permission from ref 330. Copyright 2009 Nature Publishing Group. (b) The plasmonic spectrum of a dimer can shape the fluorescence of molecules: (top panel) scattering spectra of plasmonic dimers with varying gaps; (bottom panel) the fluorescence shifts with the plasmonic spectrum. Reproduced with permission from ref 298. Copyright 2008 American Physical Society. (c) DNA origami can be used to construct plasmonic dimers that enhance fluorescence. Reproduced with permission from ref 333. Copyright 2015 American Chemical Society. (d) A judicious design of plasmonic dimers can lead to structures with very small, sub-10 nm gaps (top panel) with fluorescence enhancement that can be as large as 1500 (bottom panel). Reproduced with permission from ref 334. Copyright 2017 American Chemical Society.

dimensions, they were able to achieve tuning of the range over which the vibrational spectrum was enhanced (Figure 24c). While so far we mostly discussed the enhancement of linear optical signals by plasmonic molecules, in general there is a potential for plasmonic structures to enhance also nonlinear optical signals.7 We have already mentioned in section 2.5, the application of subradiant plasmonic modes for this purpose. In addition, plasmonic molecules have been used for the enhancement of second- and third-harmonic generation from materials inserted in their gaps.344−346 Even high-harmonic generation had been demonstrated some time ago from an argon gas interacting with plasmonic bowties,347 although this demonstration has remained debatable.348 Very recently, efficient high-harmonic generation from a silicon substrate interacting with plasmonic antennas has been demonstrated.349 Finally, two-dimensional infrared spectroscopic signals were demonstrated to be enhanced by plasmonic structures.350 There is no doubt that many applications of plasmonic molecules to nonlinear optics will appear in the future. Because the theory of symmetry is extensively used in description of the susceptibility of nonlinear materials, we expect that symmetrybased approaches as discussed in section 2.4 will be useful to describe nonlinear optical responses of matter interacting with plasmonic molecules.

focus here only on SEIRA using plasmonic molecules. Because in SEIRA only the absorption of electromagnetic energy by molecular vibrations is enhanced, the enhancement is expected to scale with the square of the local field strength. This limits the maximal possible enhancement to ∼5 orders of magnitude or so. As in other surface-enhanced phenomena, SEIRA may benefit from the large local fields within the gaps of plasmonic molecules.338,339 To test this assertion in a systematic manner, Pucci and co-workers fabricated dimers of gold rods, each of ∼1500 nm in length, and with gaps that were varied from 50 nm down to 3 nm (Figure 24a,b).340 The preparation of structures with such a large mismatch between length and gap size is challenging, and photochemical deposition was found to be a useful method for narrowing down the gaps. A layer of molecules was deposited uniformly on the plasmonic structures, and infrared absorption was measured. It was found that structures with the smallest gaps enhanced the signal by an order of magnitude compared to structures with 50 nm gaps, close to the expectation based on calculation. Several additional structures of plasmonic molecules for SEIRA were reported recently. For example, Li et al. used selfaligned techniques to form metal rod dimers that coupled either side-by-side or end-to-end.341 No big differences in SEIRA signals were observed. Brown et al. and Cerjan et al. fabricated plasmonic tetramers arranged in a cross structure with a nanogap in the center.342,343 By changing the antenna 5564


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In recent years, there has been much interest in studies of coupling between surface plasmons, either propagating or localized, and quantum emitters such as molecules.358 In particular, plasmonic molecules, in the gaps of which the electromagnetic field is very strongly localized, can serve as cavities that simplify considerably the experimental conditions required for strong light-matter interactions. In this section, we describe recent progress in using plasmonic molecules to achieve strong coupling. A useful and simple theoretical framework for understanding strong coupling phenomena is provided by the coupledoscillator model.359,360 Within the framework of this model, the cavity mode and quantum emitter excited mode are each represented by a harmonic oscillator, and the two oscillators are coupled with a rate g. The equations of motion for the coupled oscillators can be solved to obtain expressions for absorption, scattering etc. For example, the frequency dependence of light scattering from a coupled cavity−quantum emitter system is provided by the following equation:360 σsca(ω) ∝ 4

ω

(ω 2 − ω02 + iωγ0)

2

(ω 2 − ω02 + iωγ0)(ω 2 − ωpl2 + iωγpl) − ω 2g 2 (2)

In this expression, ω is the scattering frequency and ωpl and ω0 are the plasmon and quantum emitter(s) resonance frequencies, respectively, while γpl and γ0 are the corresponding line widths. Finally, g is the coupling rate, and it is given by a scalar product of the cavity’s electric field with the emitter’s transition dipole. The spectrum starts to split into two branches when the two oscillators are close to resonance and g is similar in size to the line widths or larger (Figure 25a). When g is much larger than γpl and γ0, the two branches in the spectrum become separate; this is the limit useful for quantum information applications, where manipulations on photons trapped within the cavity can be performed. While much work has been devoted to strong coupling in extended (or ensembles of) plasmonic structures,358 a more recent trend in this field has been the employment of individual plasmonic molecules for this purpose. As in other studies with individual molecules, such studies allow gauging the heterogeneities between structures. Further, they bring us closer to cavity quantum electrodynamics applications. Schlather et al. used electron beam lithography to generate gold dimers of different sizes.361 They elected to use Jaggregates of a cyanine dye as their quantum emitters due to their large oscillator strength and narrow line width. The molecules were deposited on the dimer array, and dark-field spectra of individual dimers were measured, showing a dip indicative of Rabi splitting. They obtained the energy of the lower and upper branch excitations from each dimer and plotted them as a function of the plasmon energy. Fitting this plot to the coupled-oscillator model they obtained values of the coupling rate between the plasmons and excitons, which were as high as ∼230 meV. Shegai and co-workers observed strong coupling with individual plasmonic particles, either silver nanorods362 or silver nanoprisms,363,364 in both cases employing cyanine-dye Jaggregates as their quantum emitters (Figure 25b). These authors noted the broad range of possible interaction strengths (coupling rates) between the plasmons and excitons, which

Figure 24. Surface-enhanced infrared absorption (SEIRA) in plasmonic molecules. (a,b) Dimers of long (1500 nm) rods with a small gap (schematically depicted in panel a) can lead to very large enhancements of infrared absorption (b). Reproduced with permission from ref 340. Copyright 2014 American Chemical Society. (c) Cross antennas can be tuned by varying the lengths of their arms to enhance different regions of the infrared spectrum. The panel shows absorption spectra of antennas with lengths between 600 and 1800 nm. Inset: cross antenna with L = 575 nm. Reproduced with permission from ref 342. Copyright 2013 American Chemical Society.

3.4. Strong Coupling of Plasmonic Molecules and Quantum Emitters

In the field of cavity quantum electrodynamics, emitters are placed within an optical cavity to interact with electromagnetic cavity modes.351 Approaching the limit of strong coupling between individual quantum emitters and resonant cavities is important for multiple optical applications, such as quantum information processing352,353 and quantum communication.354,355 An important manifestation of strong coupling between quantum emitters and a cavity is the phenomenon of vacuum Rabi splitting, which is an outcome of the mixing between the cavity level and the excitonic mode of the quantum emitter(s). Two excited states appear, with their energies spanning that of the original excitation of the quantum emitter. This leads to the appearance of a “transparency dip” in the spectrum of the combined system. The depth of the transparency dip is related to the strength of the coupling, which in turn depends on the ratio between the quality factor of the cavity (which is related to its damping properties) and the mode volume. In optical cavities made of, e.g., photonic crystals356 or micropillars,357 the fundamental laws of diffraction set a strict limitation on the cavity size, which cannot be smaller than half the wavelength of the interacting photon. This limits how small the mode volume can be and mandates a very high quality factor in order to attain the strong coupling regime. 5565


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Figure 25. Strong coupling of plasmonic atoms and molecules with quantum emitters. (a) A manifestation of strong coupling between a plasmonic cavity/molecule and quantum emitters should be the appearance of a split spectrum, indicating vacuum Rabi splitting. Reproduced with permission from ref 362. Copyright 2013 Nature Publishing Group. (b) Strong coupling between a plasmonic prism and J aggregates leads to a large splitting in the plasmonic spectrum. Inset: schematic of the plasmonic prism on a J-aggregate sheet. Reproduced with permission from ref 363. Copyright 2015 American Physical Society. (c,d) Silver bowties with a varying number of quantum dots positioned in their gaps show vacuum Rabi splitting in the spectrum (c). The coupling rate as a function of gap size for bowties with one quantum dot (red) and two quantum dots (green). Continuous lines are from numerical calculations, while circles are experimental results. Reproduced with permission from ref 365. Copyright 2016 Nature Communications. (e) A series of nanorods treated with solutions of J-aggregates of a range of concentration. As the concentration of the J-aggregate decreases, one arrives at the regime of coupling to a single exciton (bottom spectrum). Reproduced with permission from ref 367. Copyright 2016 American Physical Society.

their center. While the number of QDs in the cavities varied from one to a few, a major benefit of this approach was that they could be directly counted using electron microscopy. Clear Rabi splittings were observed in dark field spectra (Figure 25c). From fits to the coupled-oscillator model it was found that a coupling rate as high as 120 meV could be registered with a single QD within a bowtie cavity (Figure 25d). This result was backed by electromagnetic calculations, which showed that the coupling rate varies spatially within the cavity and is as high as the measured level in a region close to one of the bowties. Baumberg and co-workers studied NPOMs with methylene blue molecules.366 Their analysis suggested coupling could be seen even at the limit of an individual molecule, with a coupling rate of 90 meV. Very recently, Wang and co-workers showed that silver core−gold shell nanorods can serve as efficient cavities with an ultrasmall mode volumes (Figure 25e).367 By depositing J aggregates at decreasing concentrations, they arrived at the limit where the splitting seen in the spectrum could be attributed to essentially a single exciton (which likely involves ∼15 molecules363). Much improvement is required in order to bring plasmonic cavities to the level necessary for quantum optics applications. Further decrease of the cavity dimensions should make the coupling stronger. In addition, it might be possible to reduce the plasmonic line width using clever fabrication methods, although the lossy nature of plasmon excitations in metals might set a physical limit for this reduction.

may lead to different phenomena, from enhanced absorption by the quantum emitters when the interaction is weak to ultrastrong coupling, manifested as two truly separated branches in the optical spectrum. The latter limit is achieved when the coupling rate, g, is larger than the plasmon width. Where a particular system sits on this continuum of behaviors, might be deduced by accurately obtaining the microscopic parameters, although physically there is no sharp transition between them. In their most recent contribution, Shegai and co-workers were able to measure the photoluminescence of individual plasmonic particles strongly coupled to emitters.364 The splitting in photoluminescence spectra was consistently smaller than the splitting in dark-field scattering spectra, a phenomenon that remains to be explained. In all of these experiments, the interaction involved hundreds of quantum emitters or more. The employment of multiple emitters facilitates the observation of strong coupling, as the coupling rate scales with √N, N being the number of emitters. However, for quantum information operations one needs to approach the limit of a single quantum emitter coupled to the cavity. Several recent experiments attempted to approach this limit. Haran and co-workers studied silver bowtie plasmonic cavities loaded with semiconductor quantum dots (QDs).365 The choice of QDs was dictated by their relatively large oscillator strength and photostability. The bowties were fabricated by electron beam lithography, and a method was developed to insert QDs into the ∼20 nm cavities formed in 5566


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co-workers in this issue378). Under this category, one finds plasmonic structures whose resonances are tuned by modifying the properties of their dielectric surroundings. For example, the spectrum of plasmonic structures fabricated on a phase-change material could be significantly shifted by switching the material from amorphous to crystalline using laser pulses.379 It is also possible to actively change the responses of plasmonic molecules by tuning interparticle distances. This can be achieved by embedding the particles within stimulus-responsive polymers, whose structures can be modulated in response to mechanical force or a change in temperature, pH, or ionic strength. For example, stretching a polydimethoxysilane substrate was shown to modulate the optical response of heptameric plasmonic molecules, as their symmetry was lowered.380 A sophisticated novel method to dynamically tune the response of plasmonic molecules is based on DNA origami scaffolds, on which the metal particles are attached.381 In one application, the relative position of two gold nanorods was controlled through changes in the structure of the DNA scaffold, which led to changes in a CD signal.382 The developments discussed above and additional ones will surely have a strong impact on the field of plasmonic molecules in the coming years. We further expect introduction of advanced tools and concepts from ultrafast spectroscopy, quantum optics, and other advanced areas of modern physics into this field, which will yield novel and important science, as well as useful applications. We also expect integration of plasmonic molecules into larger structures, where light can be channeled and modulated. The enormous potential of this field will no doubt be the subject of multiple future reviews.

4. CONCLUSIONS AND OUTLOOK We reviewed here the exciting and growing field of plasmonic molecules. Starting with the passive aggregation of metallic particles, researchers have developed ever more sophisticated methods to design and construct structures with remarkable plasmonic properties. Either bottom-up methods based on chemistry or top-down techniques based on nanofabrication tools were used for this purpose. Over the years, we have also learned to analyze and understand the properties of plasmonic molecules, using classical electromagnetic theory as well as quantum theory. Tools from molecular spectroscopy, such as group theory, were adopted to categorize the excitations of the plasmonic molecules, and ways to predict the occurrence of more exotic spectral features, such as Fano resonances, were advanced. Sophisticated experimental methods were developed to observe and probe individual plasmonic molecules and study their properties at the nanoscale. It was realized early on that plasmonic molecules can interact with quantum objects, from molecules to semiconductor nanocrystals and more. Such interactions were found to be facilitated by the strong focusing of the fields within the gaps of plasmonic molecules and the creation of hot spots. The availability of these interactions has led to their usage to better characterize the excitations of plasmonic molecules themselves, as discussed in this review. Further, the strong fields in hot spots were shown to lead not only to familiar phenomena, such as enhanced spectroscopy, but also to novel phenomena, including hot-electron mediated chemical transformations. Finally, in recent years, the quantum nature of plasmonic molecules has been of much interest, from the effect of electron tunneling in hot spots to strong coupling with molecules. We have attempted to provide a balanced review of all of these achievements, mostly from the point of view of the basic science behind the field. Where does the future of plasmonic molecules lie? We would like to discuss in this context two emerging directions, which we believe will yield increasingly more exciting research in coming years. First, while plasmonic molecules have traditionally been made mostly from coinage metals, classes of novel materials based on other metals, as well as on ceramic and semiconducting components, are emerging.368,369 For example, the low cost of aluminum and its relatively high bulk plasmon frequency make it an attractive metal for applications. Indeed, a growing body of work shows the utility of aluminum as a plasmonic material, both in nanofabricated structures and solution-based nanocrystals.370,371 In addition, small nanoparticles of doped semiconductors of various compositions exhibit plasmonic resonances in the near- and mid-infrared,372,373 which can be obtained only with very large particles of coinage metals (see section 3.3). Transition metal nitrides (especially those of titanium and zirconium) have been shown to have superior properties compared to noble metals, including higher melting temperatures and better chemical stability.368 Finally, graphene has been shown to be an interesting plasmonic material due to its tunable infrared response.374,375 Excitation of localized plasmons in graphene nanostructures have been recently demonstrated,376 and midinfrared biosensing with graphene bioribbons was reported.377 It is expected that studies of interparticle interactions in these new materials and their analysis based on the plasmonic molecule paradigm will emerge very soon. A second interesting direction of research is the generation of dynamic or active plasmonic materials (see review by Wang and

APPENDIX: SOME INTRODUCTORY COMMENTS ON THE METHODOLOGY USED FOR STUDYING PLASMONIC MOLECULES A.1. Theoretical Methods: Mie Theory and the Static Approximation

The electromagnetic problem of light scattering by a spherical particle was solved by Mie in 1908.80 He showed that the solution can be formulated as an infinite series of the vector spherical harmonics Nn and Mn, where n is the harmonic order. These functions are the electromagnetic normal modes of the spherical particle. Vector harmonics solve the vector wave equation, while their corresponding scattering coefficients an and bn are determined by the appropriate boundary conditions. The extinction and scattering cross sections, Cext and Csca, respectively, are calculated as the flux of the energy through the arbitrary surface surrounding the particle, normalized to the flux of the energy of the excitation field, and expressed with the scattering coefficients Cext =

∞

2π k2

∑ (2n + 1)Re{an + bn}

2π k2

∑ (2n + 1)(|an|2 + |bn|2 )

(A.1)

n=1

and Csca =

∞

n=1

(A.2)

while the absorption cross-section is calculated as Cabs = Cext − Csca. The scattering coefficients an and bn are expressed in terms of Bessel functions, whose argument is the size parameter of the sphere with respect to the wavelength of the light, given by mx, where m is the ratio of the refractive indices of the metal and 5567


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the surrounding medium and x = ka, with k being the wavenumber of the excitation light, and a the sphere radius. For spheres smaller than the wavelength, the scattering coefficients are typically expanded in a series around mx. For very small spheres mx ≪ 1, and when only the leading term in the expansion is considered (of the order of x3), the only scattering coefficient surviving this long-wavelength approximation is a1, which now obtains a form that is formally equivalent to the Lorenz−Lorentz or Clausis−Mossoti formula derived in electrostatics.81 The meaning of this result is that the excitation is dominated by the N1 normal mode of the sphere, which has dipolar symmetry that corresponds to an angular momentum quantum number l = 1. Written in a different form, but within the same (lowest) order of approximation Cabs = kIm{α}

included. These contributions include radiation damping, which was mentioned above, and dynamic depolarization, which can be thought of as originating from the depolarizing field induced by different volume elements of a sphere of finite size (in contrast to the point-like sphere assumed in the electrostatic limit).89,386 They lead to a red-shift and a broadening of the particle resonance. In addition, the onset of the retardation of the electric field of light (variation of the field’s magnitude across the particle because of the finite propagation speed) leads to more complex surface charge distributions, which involve higher-order multipole terms of the expansion (A.1−A.2), namely l = 2 (quadrupole), l = 3 (octupole), etc.56,92 A.2. Theoretical Methods: Plasmon Hybridization

When two or several plasmonic atoms (particles) interact to form a cluster, the interparticle interactions facilitate formation of new normal modes whose shape is directed by the specific geometry of nanoparticle arrangement within the cluster. Within the framework of the plasmonic molecule paradigm, and in analogy to the atomic orbital hybridization approach in molecules, plasmon hybridization theory is applied to construct new normal modes of the nanoparticle cluster.60 Here, conduction electrons of metal particles are treated as a charged, incompressible, and irrotational fluid, whose deformations, described by the scalar function η, give rise to the surface charge density σ. The deformation of the charged fluid and the ∂η charge density are linked via the relation σ̇ = n0 e ∂n̂ , where n0 is the density of conduction electrons, e is the electron charge, and n̂ is the surface normal.62 In the case of molecules, all interactions between electrons and nuclei are included in the molecular Hamiltonian. Similarly, in the case of plasmonic molecules, Coulomb interactions between the conduction electrons of different nanoparticles (which are components of the electron fluid) are accounted for by the Lagrangian operator. In the most general form, the Lagrangian operator is given by

(A.3)

and

Csca =

k4 2 |α | 6π

(A.4)

where Im stands for the imaginary part and α is the dipolar polarizability of the sphere. In this equation ε − εm α = 4πa3 ε + 2εm (A.5) and is associated with the dipole moment

p = εmα E0

(A.6)

where ε is the dielectric function of the metal, εm is the permittivity of the medium, and E0 is the excitation field. That is, within the long-wavelength approximation, one can formally replace the nanoparticle with a point dipole located at its center. For shapes other than a sphere (A.3−A.4) still hold with an appropriate modification of the polarizability α. The lineshape of the plasmon dipolar mode spectrum is determined by the geometrical shape of the particle and the dielectric function of the metal. Precise knowledge of the dielectric constant is, therefore, required to describe and predict the nanoparticle’s optical properties. Because the particles of interest in plasmonics can be as small as only a few nm, i.e., much smaller than the electron mean free path, incorporation of a size-dependent correction to the bulk dielectric constant was suggested by Kreibig and co-workers.216,217 Note, however, that only a limited amount of relevant experimental data is available.383,384 As discussed in more detail in section 2.7, alternative and more rigorous approaches were developed more recently, including those based on the non-local response221,223,224 and those considering full quantum-mechanical interactions between the metal conduction electrons.219,226 Small particles of gold and silver (smaller than ca. 10 nm) are poor scatterers, such that their extinction cross-section consists mainly of absorption, and scales with the particle volume (eqs A.3 and A.5). For larger particles, scattering dominates, as it scales with the volume squared (eqs A.4 and A.5).81,92 Generally, nanoparticles having a rod shape are known to have much weaker radiative damping (i.e., loss associated with light re-emission) than spheres, which can explain their larger scattering cross sections.384,385 For particles of larger size, the electrostatic limit does not hold and contributions in addition to the static polarizability within the dipolar term a1 become significant and should be

L=

n0me 2

∫ ησ̇ dS − 12 ∫ σ|(rr⃗ )−σ(rr′⃗ ′|) dS dS′

where the first and the second terms represent kinetic and potential energy of the system, and the integration is carried out over the relevant nanoparticle surfaces.61,64 While molecular orbitals are calculated by solving the quantummechanical stationary Schrödinger equation, the normal modes of a plasmonic cluster are obtained as solutions of the classical Euler−Lagrange equations of motion. When spherical geometries are considered, e.g., clusters of spherical nanoparticles or concentric spherical shells, the plasmon hybridization method allows an analytical derivation of the charge distribution for the full set of multipole plasmon modes.61,62 Thus, the optical properties of plasmonic molecules can be evaluated to the desired accuracy. The dipolar symmetry of the charge distribution in the l = 1 mode in spherical nanoparticles couples to the electric field of light, while the modes of higher orders are optically dark under conditions where the long-wavelength approximation holds. The normal modes resulting from interaction between individual nanoparticles can be described as linear combinations of the individual nanoparticle modes.61,62,64 When the coupling is negligibly weak, for example, when the distance between nanoparticles is large or their resonances are detuned from the wavelength of light, such linear combinations involve only 5568


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The irreducible representations stand for the corresponding eigenfunctions of the symmetry operators. One-dimensional irreducible representations correspond to a single normal mode of the plasmonic molecule, while multidimensional ones correspond to modes that are degenerate according to their dimension (i.e. a two dimensional irreducible representation corresponds to doubly-degenerate modes). The degenerate eigenfunctions thus provide a symmetry-adapted basis to describe degenerate normal modes of the molecule. The degeneracy of multi-dimensional representation is lifted when the symmetry of the molecule is broken. The group-theoretical machinery390 allows us to follow associated changes in the irreducible representations using symmetry correlation tables, which indicate how the symmetry and, consequently, the optical properties of the normal modes change following geometrical changes in the structure of a molecule.65−67 In a plasmonic molecule, the interaction between nanoparticles has an electrostatic nature and depends on their relative location. The Lagrangian operator used to obtain the plasmon mode energies and normal modes within the plasmon hybridization formalism (see section A.2) commutes with transformations of the plasmonic molecule’s symmetry point group.64 To represent the normal modes of a plasmonic molecule in a symmetry-adapted basis, projection operators of the irreducible representations are constructed as discussed above. Plasmon hybridization theory predicts that normal modes of plasmonic molecules involve mixing of multipoles of different orders, induced by the electrostatic interactions. However, when a transformation to the symmetry-adapted basis set is performed, the multipoles can only mix between plasmon normal modes corresponding to the same irreducible representation. Multipoles from different irreducible representations do not mix. This renders the Lagrangian operator blockdiagonal in the new basis, which facilitates analysis of the multipole composition of plasmon resonances observed in experiments and numerical electromagnetic simulations according to their symmetry.

modes of the same order on each of the particles, as modes of different orders do not interact. For example, three dipolar modes of each individual nanoparticle, corresponding to m = +1, 0, −1, where m is the magnetic quantum number, form the bonding and anti-bonding modes of a plasmonic dimer, with charge distributions resembling parallel and anti-parallel alignment of their dipoles. Because the total dipole moment of the anti-bonding mode vanishes, it will not appear in the optical spectrum. In plasmonic molecules where the nanoparticles are located close to each other, the interaction between the modes splits and shifts their energies. Bonding modes are shifted to lower energies, while the anti-boding modes, to higher energies. In addition, coupling between modes of different orders belonging to different nanoparticles becomes significant. The latter occurs because the origins of multipole terms located on different spheres do not coincide. Such an interaction is the basis for the phenomenon of Fano lineshapes, frequently observed in optical spectroscopy of plasmonic molecules (see section 2.6). The concept of plasmon mode hybridization can be extended also beyond spherical geometries. For a rigorous description of particles having axial symmetry, elliptical rather than spherical functions can be used for the expansion of the induced charge distribution.387 A.3. Theoretical Methods: Symmetry Analysis

Group theory is frequently used in the molecular context, for example, to construct molecular or hybrid orbitals, to understand the effect of the ligand field on the reactivity and spectroscopy of transition metal complexes or to perform a vibrational normal mode analysis.388,389 It is based on a theoretical approach where the molecule in its equilibrium configuration is treated as a rigid object for which the elements of the relevant geometric symmetry group (e.g., reflections, rotations, etc.) are identified. These symmetry elements are then related to the elements of the symmetry group of the molecular Hamiltonian (e.g., atomic permutations, inversion, etc.).390 The operators representing the latter elements commute with the Hamiltonian and, therefore, share the same set of eigenvalues with the corresponding eigen functions. The elements of the symmetry group are expressed by the socalled irreducible representations, which correspond to matrices of the minimal dimension required to represent each symmetry element. The names of irreducible representations are used to label the associated molecular states according to the effect that the corresponding transformations have on the molecular wave function. The characters of the irreducible representations, which are the traces (sums of the diagonal elements) of the corresponding matrices, are used to find a symmetry-adapted basis for the molecular quantum states with the help of the projection operators. The projection operator Πi of the irreducible representation i is given by Πi =

li h

A.4. Experimental Methods: Optical Spectroscopy of Individual Plasmonic Molecules

The ability to perform optical spectroscopy on individual molecules and particles has revolutionized chemical physics in the last two decades.391 Single-particle spectroscopy has allowed researchers to dissect heterogeneous ensembles and separately characterize groups of particles within the ensemble and has led to important observations related to the interaction of particles with their environment, as well as their size and shape distributions. Methods for studying plasmonic molecules one by one have also been developed and have become important tools in the experimental arsenal; in this section, we will introduce briefly the basic principles of these experimental techniques. Dark-field microscopy was adapted as a method to study the scattering spectra of plasmonic particles and molecules. This type of microscopy generates a background-free image of objects that scatter the illumination light. In particular, darkfield illumination requires blocking the central part of the light cone impinging on the sample, allowing only oblique rays from every azimuth to pass through. If no sample is present, the field of view would appear dark, but if objects in the sample plane scatter light, they would appear as bright spots in the image. Now if the light scattered from a single object in the image plane is dispersed using a spectrograph, one obtains the

∑ χi (R) × PR R

where li is the dimension of the irreducible representation, h is the dimension of the group, R enumerates the symmetry operators PR, and χi(R) is its character in the irreducible representation. The projection operator is applied to a set of basis functions of the individual nanoparticle plasmon multipole modes. 5569


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scattering spectrum of the object. The first application of this simple but very effective method in plasmonics was reported by Schultz et al. in 2000.392 It was then used by the same group to show shape effects in plasmon spectra of individual particles,55 as well as by Sönnichsen et al., to study plasmon dephasing in gold nanorods.385 Dark-field spectroscopy has since become the method of choice for studying the spectra of individual plasmonic particles or clusters.393 A restriction of this method is its limitation to relatively large particles, whose scattering cross section is significant enough to be registered. Particles smaller than ∼30 nm are difficult to observe with this technique. Further, even for large particles, it is sometimes interesting to obtain the full extinction spectrum, which includes not only scattering but also absorption. If the extinction cross-section is significant, it is possible to perform a direct measurement of the extinction spectrum by comparing the light transmitted through the sample with and without the object.393,394 However, if the extinction cross-section is small, this method does not work. Photothermal imaging, first introduced by Orrit and coworkers,395 can solve this problem. In photothermal imaging, the scattering of one laser beam from the sample depends on the absorption of a second laser beam by objects in the sample and the ensuing heating. Yorulmaz et al. employed photothermal imaging in combination with a broadband heating laser, which allowed them to obtain the full absorption spectra of individual plasmonic particles396 and plasmonic molecules.205

dipolar mode due to plasmon hybridization in a dimeric plasmonic molecule can be measured with STEM-EELS.131 More recently, this measurement was extended by Barrow et al. to more complex plasmonic molecules, such as trimers and tetramers.67 More details can be found in the excellent review of Cherqui et al.400 and in the thematic sections of this review. A second electron microscopy method that can be used to image plasmonic modes is cathodoluminescence (CL). In this technique, the electron beam excites the sample locally, and light emitted from the sample is collected by a photomultiplier or dispersed by a spectrograph and collected by a camera, generating a spectrum of the emission from the sample. CL spectroscopy can be performed in a scanning electron microscope, making it more accessible than EELS. However, the CL signal is weaker.121 Nevertheless, it is possible to use CL to map plasmonic modes in individual particles401 and more complex plasmonic molecules.402 The comparison of EELS and CL signals can be useful for the identification of dark and bright modes.403

A.5. Experimental Methods: Spectroscopy within the Electron Microscope

Corresponding Authors

ASSOCIATED CONTENT Special Issue Paper

This paper is an additional review for Chem. Rev. 2018, volume 118, issue 6, “Plasmonics in Chemistry”.

AUTHOR INFORMATION *G.H.: E-mail, [email protected]. *L.C.: E-mail, [email protected].

While optical spectroscopy provides a relatively facile access to the excitations of plasmonic molecules, there are two important limitations: First, it probes the signature of the plasmonic field in the far-field, namely after it propagated away from the nanosized system. Second, it can observe only “bright plasmonic modes”, namely modes that interact with light because their total dipole moment is finite, while “dark modes” that cannot interact with light are not observed. Both limitations can be overcome by using an electron beam, rather than light, to excite plasmonic modes. Because an electron beam can be focused to a subnanometer spot, it can excite and image plasmonic modes locally, and the limitation to bright modes does not exist as the mode of interaction with the electrons is different than with light. Colliex and coworkers reported a breakthrough study of plasmonic fields with an electron beam in 2007.125 They performed electron energy loss spectroscopy (EELS) within a scanning transmission electron microscope (STEM) to image and map the plasmonic fields around silver triangles. In STEM-EELS, a focused electron beam is used to scan the surface of the sample, and electrons that scatter inelastically from the sample are detected on a spectrometer. An energy loss spectrum can then be plotted at each point in the image. While EELS measurements of surface plasmons on metallic particles had been reported previously,397,398 a novelty of the work of Nelayah et al.125 was that they were able to measure spectra down to 1 eV and with a spatial resolution of ∼1 nm. Since then, the method has improved significantly, and with a new generation of aberrationcorrected electron microscopes, spectra with a resolution of a few tens of an eV can be readily recorded (a record resolution of ∼10 meV was reported by Krivanek et al.399). Spectra from more complex structures have been measured. Thus, for example, Koh et al. showed that the spectrum of the dark

ORCID

Gilad Haran: 0000-0003-1837-9779 Lev Chuntonov: 0000-0002-2316-4708 Notes

The authors declare no competing financial interest. Biographies Gilad Haran is a professor in the department of Chemical and Biological Physics of the Weizmann Institute of Science. He did his Ph.D. at the Weizmann Institute with Professors Ephraim KatchalskyKatzir and Elisha Haas. He was then a postdoctoral fellow with Professor Robin Hochstrasser at the University of Pennsylvania. Gilad Haran’s lab is using single-molecule spectroscopy to study a broad range of phenomena, from protein folding and function to molecular dynamics on metal surfaces and plasmonics. Lev Chuntonov received his Ph.D. degree from TechnionIsrael Institute of Technology with Professor Zohar Amitay, where he worked on coherent control of multiphoton excitation using shaped femtosecond pulses. He was a postdoctoral fellow at the Weizmann Institute of Science with Professor Gilad Haran and at University of Pennsylvania with Professor Robin M. Hochstrasser. He is currently an assistant professor in the Schulich Faculty of Chemistry at the TechnionIsrael Institute of Technology, where he couples his interests in plasmonics and ultrafast laser spectroscopy.

ACKNOWLEDGMENTS This work was partially funded by grant no. 2016167 from the US−Israel Binational Science Foundation to Lev Chuntonov. We thank Dr. Nir Zohar for his help with some of the graphics. 5570


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