Strong light-matter coupling between plasmons in individual gold

Subscriber access provided by University of South Dakota

Communication

Strong light-matter coupling between plasmons in individual gold bipyramids and excitons in mono- and multilayers of WSe2 Michael Stührenberg, Battulga Munkhbat, Denis G. Baranov, Jorge Cuadra, Andrew B. Yankovich, Tomasz J. Antosiewicz, Eva Olsson, and Timur Shegai Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b02652 • Publication Date (Web): 06 Aug 2018 Downloaded from http://pubs.acs.org on August 8, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Strong light-matter coupling between plasmons in individual gold bipyramids and excitons in monoand multilayers of WSe2 Michael Stührenberg1, Battulga Munkhbat1, Denis G. Baranov1, Jorge Cuadra1, Andrew B. Yankovich1, Tomasz J. Antosiewicz1,2, Eva Olsson1, and Timur Shegai1,* 1Department of Physics, Chalmers University of Technology, 412 96, Göteborg, Sweden. 2Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland.

ABSTRACT

Monolayer transition metal dichalcogenides (TMDCs) have attracted a lot of research attention recently, as motivated by their remarkable optical properties and potential for strong light-matter interactions. Realization of strong plasmon-exciton coupling is especially desirable in this context as it holds promise for enabling room temperature quantum and nonlinear optical applications. These efforts naturally require investigations at a single nanoantenna level, which in turn should possess a compact optical mode interacting with a small amount of excitonic material. However, standard plasmonic nanoantenna designs such as nanoparticle dimers or

ACS Paragon Plus Environment

1

Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 28

particle-on-film suffer from misalignment of the local electric field in the gap with the in-plane transition dipole moment of monolayer TMDCs. Here, we circumvent this problem by utilizing gold bipyramids (BPs) as very efficient plasmonic nanoantennas. We demonstrate strongcoupling between individual BPs and tungsten diselenide (WSe2) monolayers at room temperature. We further study the coupling between multilayers of WSe2 and BPs to elucidate the effect of the number of layers on the coupling strength. Importantly, BPs adopt a reduced symmetry configuration when deposited on WSe2, such that only one sharp antenna tip efficiently interacts with excitons. Despite the small interaction area, we manage to achieve strong coupling with Rabi splitting exceeding ~100 meV. Our results suggest a feasible way towards realizing plasmon-exciton polaritons involving nanoscopic areas of TMDC, thus pointing toward quantum and nonlinear optics applications at ambient conditions.

KEYWORDS: Strong coupling, TMDC, WSe2, exciton, gold bipyramid, plasmon resonance


2

Page 3 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

INTRODUCTION

Interactions between light and matter are essential to many contemporary scientific disciplines. An especially interesting regime of light-matter interactions is achieved when the rate of coherent energy exchange between matter and optical excitations becomes faster than any of their intrinsic dissipation rates. Such regime is called strong coupling. In contrast to the weak coupling regime, where only modified spontaneous emission is observed (the Purcell effect) 1, the strong coupling regime leads to formation of new eigenstates of the coupled system, so called cavity-exciton polaritons, which have intermixed light and matter character. Strong emittercavity coupling enables realization of ultrafast single-photon switches 2 and quantum information processing schemes 3. These and other important quantum optical observations, however, are limited to cryogenic temperatures and ultra-high vacuum 4-6. The coupling strength is determined as = √ │ │ ∝ ⁄ with and being the

vacuum field and the mode volume of the resonator, the transition dipole moment of the

quantum emitter, and the number of emitters coherently contributing to the interaction with the cavity 7, 8. To reach strong coupling, the coupling strength must exceed the polariton decay rate. One way to achieve this is to employ optical microcavities, such as Fabry-Pérot cavities bounded

by distributed Bragg reflectors or metallic mirrors, loaded with a large number of organic chromophores

9-12

. Another possibility is to utilize plasmonic nanostructures, which recently

were shown to reach the strong and even ultra-strong coupling regimes upon interaction with Jaggregates at room temperature

13-16

. These experiments, however, require large numbers of


3

Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 28

organic molecules arranged in a disordered manner to interact with an optical mode. TMDCs represent another promising class of materials suitable for strong light-matter coupling that, due to high transition dipole moment, relative inertness and optical stability, possess a number of advantages over organic chromophores 17, 18. Several recent studies report observation of strong coupling between TMDCs and microcavities photonic arrays

22, 23

19-21

as well as diffractive plasmonic and

. Several recent works also demonstrated strong coupling of TMDCs to

localized modes of individual plasmonic nanoantennas 24-27. In this context, it is important to emphasize that for studying quantum optical, nonlinear and saturation effects, for example photon blockade

28

, strong coupling should be realized with a

small number of quantum emitters, ideally with a single one. Plasmonic nanoparticles offer a feasible platform for exploration of these concepts, as they are able to confine electromagnetic fields down to deep subwavelength volumes

29

. Room temperature strong coupling on a single

quantum emitter level was reported only for plasmonic nanoantennas with tight gaps

30-33

.

Although this approach has resulted in several remarkable observations, it still has a number of disadvantages related to the lack of reproducible control, scalability and fabrication-related issues at such small scales. Here, we take an alternative route and utilize a simple and reproducible antenna design based on chemically synthesized gold bipyramids. We achieve single hot-spot strong coupling of excitons in mono- and multilayer WSe2 to plasmons in Au BPs under ambient conditions. BPs are designed and fabricated to have plasmonic resonances optimally overlapping with the A-exciton absorption line of WSe2. Compared to other common plasmonic nanostructures such as nanorods, nanospheres and nanoprisms, BPs possess superior plasmonic features, such as narrow


4

Page 5 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

plasmonic resonances and adaptation of asymmetric configuration with respect to a supporting surface

34, 35

(see Figure 1). Because of this asymmetry, only one of a BP’s sharp tips interacts

strongly with the exciton material. At the same time the sharp tip forms a tightly confined electromagnetic hot-spot. Such a combination effectively reduces the interaction volume and thereby the amount of WSe2 participating in the coupling. Experimentally measured Rabi splittings extracted from anti-crossing curves consisting of several hundred individual BPs darkfield (DF) scattering spectra reach values up to ∼85-105 meV, depending on the number of WSe2 layers. Numerical calculations confirm the formation of polaritonic states in both mono- and multilayer WSe2 configurations. In the latter case strong coupling occurs despite the absence of a direct band gap transition.

RESULTS

To study strong light-matter coupling of plasmons with excitons within a single hot-spot, hybrid samples were prepared by depositing Au BPs on mechanically exfoliated WSe2 flakes. The BPs were synthesized using a wet chemistry approach

34, 36

, which allows to accurately tune the

particle’s aspect ratio and thereby the plasmon resonance frequency. The average BP used in our measurements is around 110 nm × 40 nm with an aspect ratio of 2.75 as determined from scanning electron microscopy (SEM) images. Each BP has a pentagonal base with two mirrored flat-sided cones 35. Bright field (BF) and high angle dark field (HAADF) scanning transmission electron microscopy (STEM) data shows that our BPs possess high quality crystal order and very sharp tips with a radius of about 5 nm (see Figure 1a and Figures S5-6). This leads to a narrow


5

Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 28

plasmon line width of ≈110 meV (see Figure 1b) in comparison to other common single crystalline plasmonic nanostructures, such as nanorods 24 and nanoprisms 27.

Similarly to nanorods, BPs support longitudinal and transverse plasmonic resonances. In our experiments, it is only the longitudinal plasmon mode at ∼1.67 eV, which overlaps with the Aexciton of WSe2. The transverse plasmon at ∼2.25 eV does not contribute to the coupling process. Excitation at the plasmon resonance of the BP in an index-matched environment results in two hot-spot regions localized at the sharp tips

37

. However, in our experiments only one of

the ten BP facets is actually in contact with the substrate, as evidenced from TEM. This arrangement breaks the symmetry and only one tip of the BP is in contact with the surface, while the other one is lifted above the substrate by the full transverse diameter (up to ~40 nm). Thus, only one of the two hot-spots interacts with the underlying material efficiently (see Figure 1c).


6

Page 7 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Figure 1. Single hot-spot strong light-matter coupling. (a) BF STEM image of the tip of a BP showing a very sharp tip (~5 nm radius). Inset shows a SEM image of a single BP (scale bar = 50 nm). (b) Dark-field scattering spectrum of a single bipyramid on SiO2 substrate, showing a longitudinal plasmon resonance peak with a line width of 110 meV (black). Photoluminescence spectrum of the A-exciton in a WSe2 monolayer (red), which overlaps well with the plasmon resonance and has a line width of about 40 meV. (c) Schematic of a gold bipyramid positioned on top of an N-layered WSe2 flake. In our experiments N=1-4 or 8. (d) Polarization resolved dark-field scattering spectra of the coupled system. Inset shows a corresponding SEM image (scale bar = 50 nm). The orange and blue arrows show polarizations directions along and perpendicular to the long axis of the BP, correspondingly.

WSe2 flakes were mechanically exfoliated from a bulk crystal and then transferred onto a Si/SiO2 substrate. Due to less strain and fewer defects, exfoliated flakes offer superior quality in comparison to other fabrication methods such as chemical vapor deposition (CVD) 38. However, exfoliated flakes suffer from random orientation and small lateral dimensions typically limited to a few tens of microns. Combined photoluminescence (PL), optical contrast (see Figure S1) and reflection measurements allow determining the number of WSe2 layers. The contrast in PL signal arises from the fact that the band structure of TMDCs strongly depends on the number of layers in a small N limit, as the material evolves from an indirect for N>1 to a direct bandgap for N=1 semiconductor

39, 40

. The excitons in TMDCs have exceptionally high binding energies and are

stable even under ambient conditions at which all our experiments have been conducted. The Aexciton emission of a monolayer shows a single peak at around =1.67 eV with a narrow PL line width of about 40 meV (Figure 1b). We also used reflection measurements to determine the A-exciton line width of =44 meV in a WSe2 monolayer (see Figure S2). Both values agree well with the literature 18, 25, 41, 42.

We further used polarization-dependent single particle dark-field (DF) scattering to investigate


7

Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 28

the coupled and uncoupled plasmon-exciton systems. The optical data was complemented by morphological SEM analysis for each individual BP. To reach the strong coupling regime, the two uncoupled modes need to exhibit simultaneous spectral and spatial overlap. The former was achieved by tuning the plasmon resonance of a BP to the A-exciton line of the WSe2 (Figure 1b), while the latter was achieved by depositing the BP directly on the 2D material, so that the excitons in the layer are exposed to plasmonic near-fields (Figure 1c). DF spectra reveal the appearance of two new optical modes separated by about 85 meV (Figure 1d). These new modes show a strong polarization dependence and can be probed only along the long axis of the BP (0⁰, Figure 1d), whereas no spectral response was observed along the short axis (90⁰, Figure 1d). It is also important to mention that during the synthesis, BPs are capped with a thin layer of CTAB ligand molecules, which prohibits a direct contact between WSe2 and nanoparticles by leaving a sub-nanometer gap 43, 44.

To ensure that the coupled system is in the strong coupling regime, the anti-crossing of its hybrid resonances needs to be analyzed. The fabrication process allows for tuning the size of the BP, but in any nanoparticle batch there is always a slight distribution of aspect ratios, which leads to a slight particle-to-particle variation in the plasmon resonance. This allows us to probe particles with different plasmon-exciton detunings and thus to reconstruct the anti-crossing. Figure 2a shows DF scattering spectra for several coupled systems with different geometric aspect ratios revealed by the corresponding SEM images. The resulting spectra clearly exhibit different plasmon-exciton detunings. For large aspect ratio BPs, the plasmon energy is lower than the exciton energy, = − < 0 (Figure 2a, red line). In this regime, scattering by the lower polariton (LP) is much higher than that of the upper polariton (UP). With a decreasing aspect ratio, the plasmon shifts to higher energies until it matches the exciton energy, = 0. In this ACS Paragon Plus Environment

8

Page 9 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

case both the LP and UP become almost identical in terms of scattering intensity and spectral shape (Figure 2a, green line). With even smaller aspect ratios the plasmon experiences a further blue shift giving rise to a positive detuning, = − 0, and a larger scattering amplitude for the UP in comparison to the LP (Figure 2a, purple line). A clear anti-crossing behavior between LP and UP is seen, which is a typical characteristic of strong coupling.

Figure 2. Strong coupling of bipyramid plasmons with excitons in monolayer WSe2. (a) Experimentally measured DF scattering spectra with bipyramids of different aspect ratios and resonance frequency. Each spectrum has been probed along the long axis of the BP. Insets are corresponding SEM images with denoted aspect ratio (scale bar = 50 nm). LP and UP denote the lower and upper polariton, respectively. (b, c) The corresponding FDTD simulations showing scattering (b) and absorption (c) spectra for the model systems mimicking the experimental configuration in (a).

The detuning between the plasmonic and excitonic resonance furthermore determines the composition of final polaritonic states, which at zero detuning are equally composed of the


9

Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 28

plasmon and the exciton contributions (shown in Figure S3). In a strongly blue-detuned system ( ≫ ) the upper polariton is mostly plasmon-like, while the lower polariton is mostly excitonic in nature. For a strongly red detuned system ( ≪ ), the polariton composition is

reversed.

Numerical calculations, performed using the finite-difference time domain (FDTD) method (see Methods), reproduce experimentally measured DF scattering spectra by using geometrical parameters extracted from SEM images (Figure 2b). However, an apparent splitting in scattering can be a result of a Fano resonance (so-called electromagnetically induced transparency) or even enhanced absorption 45. To verify that the system is indeed strongly coupled, we complemented the scattering data with calculated absorption spectra (Figure 2c). For the case of a weakly coupled system the absorption spectrum should show a single peak at the plasmon resonance of the metal nanoparticle. For the case of our BPs, however, we found a similar anti-crossing behavior as for scattering (Figure 2c). The shape of the absorption spectra is a clear indication that the system is in the strongly coupled regime.

To further analyze the spectroscopic data, we employ the coupled oscillators model in Hamiltonian representation 7. The coupled system satisfies the following eigenvalue problem:

−

!"

#

−

$

#

% &(' ) = ± &(' ) ±

±

(1)

where and are the plasmon resonance energy and dissipation rate, and are the

exciton energy and its dissipation rate, is the coupling strength and + and , are Hopfield


10

Page 11 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

coefficients. Diagonalization of this Hamiltonian yields two polaritonic eigenvalues, ± : ± =

-!" .-$ #

#

± /# + 2 3 − # 5 − 67 1

4

(2)

corresponding to the energies of the UP and LP. The two eigenvectors 8+, ,:;± reflect the

composition of the resulting polaritonic eigenstates. At zero detuning, − = 0, the above expression yields the value of the vacuum Rabi splitting:

Ω = /4# −

5 !" > $ 6 2

?

(3)

at the position of the avoided crossing.

For each individual strongly coupled BP we obtain experimentally measured frequencies of the UP (. ) and LP (> ). In Figure 3a-d we show the dispersion of the upper and lower polariton

energies versus the bare plasmon energy , which can be determined via = . + > −

. The UP and LP values were extracted from DF scattering data of BPs deposited on several

different mono- and multilayer flakes (N=1…4). The data includes a statistically meaningful number of individual BPs for N=1...3. A slightly smaller number of points for N=4 is explained by a relative complexity of isolating this specific multilayer. In addition, data for N>4 is hard to access because of the complexity of differentiating between higher order multilayers due to low reflectivity contrast and almost complete absence of PL signal. However, to complement the N=1…4, we have measured scattering spectra from several BPs positioned on top of a much thicker multilayer, whose exact thickness was determined by atomic force microscopy (N=8) rather than optical contrast. This last experimental point attempts to measure the asymptotic Rabi


11

Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 28

splitting in the system with a completely saturated mode volume (see Figure 3e).

By fitting the experimentally measured dispersions with the eigenvalues of Eq. (2), we extract values for the vacuum Rabi splitting Ω and the coupling strength for every number of layers. In the fitting procedure, the plasmon line width measured as the full width of the scattering spectrum of an uncoupled BP ( ≈110 meV), and the exciton line width determined from reflection spectra (see Figure S2) were used. For BPs placed on a monolayer WSe2 ( =1.67 eV,

=50 meV) we found a Rabi splitting of Ω = 83.1 ± 0.2 meV and coupling strength =

44.8 ± 0.5 meV (Figure 3a,f). These values reflect that Ω F 2 and show that dissipation has only a minor effect around zero detuning. The resulting value of Rabi splitting slightly exceeds the polariton line width,

!" . $

#

≈77.5 meV, allowing us to claim being at the onset of the strong

coupling regime. At the same time, the Rabi splitting obtained in this case is, to the best of our knowledge, the highest reported so far for an open plasmonic cavity coupled to excitons in a WSe2 monolayer.


12

Page 13 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Figure 3. Anti-crossing and Rabi splitting on multilayer WSe2. (a)-(e) Dashed blue lines denote the exciton energy and the diagonal dashed green line indicates the plasmon energy. Open symbols represent UP (orange) and LP (purple) energies obtained from DF scattering spectra of individual hybrid nanoparticles. The solid lines show the UP and LP dispersions for N=1-4 and 8 layers of WSe2, respectively, obtained using the coupled oscillator model, Eq. (2). Black markers in (a)-(d) show corresponding FDTD simulations. (f) Rabi splitting and coupling strength as a function of number of WSe2 layers, extracted from DF scattering data from (a)-(e) using the coupled oscillator model. The data suggest saturation of both Ω and at around N=4.

Furthermore, despite the absence of a direct bandgap, we observed similar anti-crossing behavior in 2-, 3-, 4-, and 8-layer WSe2 systems (Figure 3b-e). With an increasing number of layers, the exciton shifts to lower energies and may be expected not to match the plasmon resonance any longer. However, due to the increasing amount of high refractive index material (WSe2), the plasmon energy experiences a similar red-shift (visible in Figure 3 as the gradual red-shift of the experimental points along the G-axis), which allowed us to use the same batch of BPs for all measurements. The change of the refractive index should also influence the plasmon line width, however, simulations showed that, most likely due to the asymmetric shape and only a small contact area, the plasmon line width remains nearly unchanged and was kept constant throughout the whole analysis. The calculated DF scattering spectra for the case of multilayers are shown in the Supporting Information (Figure S4), while the UP and LP energies for the calculated spectra are shown as black markers in Figure 3a-e. Overall, we observe good agreement between experimental and calculated spectra.

It is intriguing to observe that the magnitude of Rabi splitting, as well as the coupling strength increase with the number layers, as shown in Figure 3f. The Rabi splitting at first increases in a nearly linear fashion from a monolayer up to four layers. The coupling strength exhibits a


13

Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 28

somewhat nonlinear dependence in the beginning with the smallest change from a mono- to a bilayer, thus from a direct bandgap to an indirect bandgap material, and then increases almost linearly with more layers. Remarkably, both the Rabi splitting and the coupling strength seem to saturate at around N=4. This is demonstrated by performing an experiment on a much thicker flake (N=8), which shows Rabi splitting and coupling strength values similar to those obtained for the four layer sample (see Figure 3e,f).

To interpret our observations, we have calculated the plasmonic mode volume for our system under study. The resulting dependence of the BPs’ mode volume on the number of WSe2 layers underneath the nanostructure is presented in Figure 4a along with the corresponding vacuum field, . The mode volume varies from 3150 nm3 for a BP on top of a monolayer down to 1750 nm3 for four layers of WSe2 and slightly smaller for even higher number of layers. These values are small compared to other typical nanostructures, e.g. nanoprisms

15

or nanorods

25

, as

well as much smaller than the physical volume. The resulting vacuum field, which corresponds to the mode volumes, exhibits clear signs of saturation (Figure 4a). The mode volume was calculated using an integral of the electromagnetic energy-density in the system comprising a BP nanoantenna positioned on top of a high-refractive index material with its excitonic band switched off (see Methods). The energy density distribution around the nanostructure verifies that even though the BP possesses two regions of strong field enhancement, only one of them is in close vicinity to the underlying 2D material (see Figure 4d, note the log scale). The other tip of the bipyramid is lifted from the substrate by about 30-40 nm and thus does not significantly interact with excitons. This effectively limits the amount of excitonic material involved in the interaction with a plasmon to only that near the bottom hot spot (Figure 4d,e). Furthermore, with an increasing number of WSe2 layers, the plasmonic mode gets more localized inside the TMDC


14

Page 15 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

effectively decreasing the mode volume, yet simultaneously increasing the amount of excitonic material available for coupling. Consequently, both factors join to increase the overlap of the plasmonic mode and the 2D material, increasing the number of excitons involved in the coupling process. The combination of the reduced mode volume and the higher number of excitons confirms the experimentally determined increase of Rabi splitting with a higher number of WSe2 layers. The larger number of WSe2 layers means that coherent coupling occurs within a greater amount of excitonic material. However, the decrease of the induced electric field away from the nanoantenna means that the coupling strength decreases as one moves away from the BP (see Figure 4b). The coupling strength to the top-most layer is approximately constant at 0.5 meV per 1 D of an exciton’s transition dipole moment, but decreases by approximately 20% for every subsequent layer. This means that despite the increased vacuum field and more excitonic material, the coupling efficiency per amount of used WSe2 decreases with the number of layers. This decreasing effect is the predominant cause of the rapid saturation of observable Rabi splitting at 4 layers, a value twice smaller than the calculated saturation thickness for the vacuum field.

Knowledge of the mode volume, the vacuum field (Figure 4a), and the plasmon mode overlap with the excitonic material

46

together with the experimentally measured coupling strength

(Figure 3f) allows estimating the coherent transition dipole moment of WSe2 in accordance with = HIJKL /

ℏ-

#NN$ O

, where H is the overlap function which accounts for the placement of an

exciton outside of the maximum energy density of the BP’s mode. For a monolayer IJKL = 87 D, as the overlap between the mode and the excitonic material reduces the maximum coupling strength to 0.52 meV/D (Figure 4b). We further extend this analysis to multilayers and


15

Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 28

plot corresponding coherent transition dipole moment values in Figure 4c. The calculation is based on the maximum coupling strength of WSe2 to the cavity factoring into account the overlap function H, as plotted in Figure 4b. The obtained values for the dipole moment are about twice smaller than those reported recently for Ag nanoprism − J-aggregate 15 and plasmon − WS2 hybrids

27

, indicating that BPs have a more compact optical mode in comparison to Ag

nanoprisms and that they can reach strong coupling with smaller amount of excitonic material.

Figure 4. Mode volume and exciton density in the coupling process. (a) Dependence of the BP mode volume (left y-axis, squares) and vacuum field (right y-axis, diamonds) on the number of WSe2 layers underneath the nanostructure. (b) Partial maximum coupling strength of a BP to a 1 D exciton in each layer. The coupling decreases the farther a layer is from the BP with each step decreasing the coupling by approximately 20%. (c) Estimation of the coherent transition dipole moment needed to assure the measured coupling strength using the coupling strengths in the top WSe2 layer in panel (b). (d) Energy density cross section of the dipolar quasi-normal mode of the bipyramid on top of a WSe2 monolayer in log10 scale, the inset shows a magnification of the tip near the 2D material. (e) Energy density cross section through the middle of the WSe2 monolayer in linear scale.


16

Page 17 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

DISCUSSION

In conclusion, we have demonstrated strong coupling of excitons in mono- as well as multilayers of WSe2 to plasmon resonances in gold BPs. The asymmetric geometry of the BP positioned on top of WSe2 results in a single hot-spot interaction volume that greatly reduces the amount of excitonic material involved into plasmon-exciton interaction. Importantly, the Rabi splitting in our hybrid systems is observed despite the indirect bandgap of multilayer material, demonstrating that it is the absorption rather the emission strength, which is of relevance for plasmonic strong coupling applications. We also note that recent theoretical predictions show that quantum optical phenomena, such as antibunching of coherently scattered light, can be observed from plasmonic nanoantennas strongly coupled not only to individual but also to several quantum emitters

47

. Our study shows a practical approach towards realization of such

strongly coupled nanophotonic systems for further explorations in the nonlinear and quantum optical domains at ambient conditions and by using a very simple and robust single nanoparticle antenna design.

METHODS

Sample preparation: WSe2 flakes were mechanically exfoliated onto (polydimethylsiloxane) PDMS stamps using a scotch-tape method and transferred on thermally oxidized Si substrate (SiO2 thickness 55 nm). Gold BPs were synthesized using a seed-mediated method in aqueous solution according to the literature

34, 36

. Subsequently, the BPs solution was drop casted on the

WSe2 flakes to prepare the hybrid samples. The concentration of BPs in the solution was


17

Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 28

adjusted such that the density of BPs on the sample surface was suitable for single particle optical microscopy measurements.

STEM experiments: STEM specimens were prepared by dispersing the Au BP containing solution onto 15 nm thick SiN membrane TEM windows and allowing the solution to dry. STEM experiments were performed using a FEI Titan 80-300 TEM/STEM microscope operated at 300 keV. The instrument is equipped with a field-emission electron source and a probe aberration corrector, allowing for sub-Ångstrom STEM spatial resolution. Images were acquired using a probe convergence semi angle of ~24.5 mrad and both the BF and HAADF detectors.

Dark-field measurements: An upright microscope (Nikon Eclipse LV150N) equipped with a (100 W) halogen lamp was used in a DF mode to excite the sample with unpolarized white light through an objective lens (Nikon TU Plan ELWD 100× NA=0.8) The scattered signal was collected via the same objective lens in a hyperspectral configuration 15. Specifically, the signal is directed through a liquid crystal filter (LCF) (VariSpec SNIR, 650-1100nm), which also acts as a linear polarizer. Images are collected on an EM-CCD camera (Andor, iXon DV887) synchronized with the LCF, which allows to record series of optical images as a function of wavelength. The final DF spectra are obtained by processing the images.

Numerical Simulations: We performed numerical calculations of the induced quasi-normal modes of the nanoprisms using the finite-difference time-domain method (FDTD Solutions, Lumerical). The approximate dimensions of the simulated bipyramids were taken from SEM images and the edge lengths were adjusted slightly to obtain spectral overlap of the dipolar LSPR with the exciton of a single WSe2 monolayer. The simulated Au bipyramid is 115 nm in length (along the long axis) and the diameter of the circle which circumscribes the widest part of the


18

Page 19 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

bipyramid is 41 nm (aspect ratio of 2.8). The bipyramid has 5-fold rotational symmetry; the edges have a radius of curvature of 5 nm and the ends 7.5 nm. The bipyramid is placed, as in experiments, on top of a stack of three materials: a 1 nm CTAB-mimicking layer (n = 1.45), a WSe2 mono- or multilayer (thickness increases in increments of 0.7 nm), and a glass substrate with a refractive index of 1.45. The permittivity of gold is taken from Johnson and Christy 48 and that of the WSe2 is based on our reflection measurements and literature 49. The evolution of the mode volume with a changing environment was calculated using the approach for dispersive weakly radiating cavities

50

. Due to the asymmetry of the mode induced by the presence of the

substrate near one of a bipyramid’s ends and small feature sizes, for mode volume calculations we use mesh refinement down to 0.1 nm in all three directions where one of the tips of the bipyramid interacts with WSe2. The rest of the bipyramid is then meshed with 0.2 nm resolution.

ASSOCIATED CONTENT Supporting Information Available: More detailed information about the samples including bright-field image, exciton bandwidth extraction, reflection spectrum, polariton fractions, direct comparison of experimental vs simulated scattering spectra and STEM images of the Au BPs. Corresponding Author *The correspondence should be addressed to T.S. [email protected]

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.


19

Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 28

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS We acknowledge financial support from Swedish Research Council (VR) and Engkvist Foundation. TJA acknowledges financial support from the Polish National Science Center via the project 2017/25/B/ST3/00744.

REFERENCES

1.

Purcell, E. M. Physical Review 1946, 69, 37-38

2.

Volz, T.; Reinhard, A.; Winger, M.; Badolato, A.; Hennessy, K. J.; Hu, E. L.; Imamoglu, A. Nat Photon 2012, 6, 605-609. Sillanpää, M. A.; Park, J. I.; Simmonds, R. W. Nature 2007, 449, 438. Yoshie, T.; Scherer, A.; Hendrickson, J.; Khitrova, G.; Gibbs, H. M.; Rupper, G.; Ell, C.; Shchekin, O. B.; Deppe, D. G. Nature 2004, 432, 200-203. Groblacher, S.; Paterek, T.; Kaltenbaek, R.; Brukner, C.; Zukowski, M.; Aspelmeyer, M.; Zeilinger, A. Nature 2007, 446, 871-875. Faraon, A.; Fushman, I.; Englund, D.; Stoltz, N.; Petroff, P.; Vuckovic, J. Nat Phys 2008, 4, 859-863. Törmä, P.; Barnes, W. L. Reports on Progress in Physics 2015, 78, 013901. Baranov, D. G.; Wersäll, M.; Cuadra, J.; Antosiewicz, T. J.; Shegai, T. ACS Photonics 2017, 5, 24. Lidzey, D. G.; Bradley, D. D. C.; Skolnick, M. S.; Virgili, T.; Walker, S.; Whittaker, D. M. Nature 1998, 395, 53-55. Hobson, P. A.; Barnes, W. L.; Lidzey, D. G.; Gehring, G. A.; Whittaker, D. M.; Skolnick, M. S.; Walker, S. Applied Physics Letters 2002, 81, 3519-3521.

3. 4. 5. 6. 7. 8. 9. 10.


20

Page 21 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.

22. 23. 24. 25. 26.

27. 28. 29. 30. 31. 32.

33.

Schwartz, T.; Hutchison, J. A.; Genet, C.; Ebbesen, T. W. Physical Review Letters 2011, 106, 196405. Barachati, F.; Simon, J.; Getmanenko, Y. A.; Barlow, S.; Marder, S. R.; Kéna-Cohen, S. ACS Photonics 2018, 5, 119-125. Balci, S. Optics Letters 2013, 38, 4498-4501. Schlather, A. E.; Large, N.; Urban, A. S.; Nordlander, P.; Halas, N. J. Nano Lett. 2013, 13, 3281–3286. Zengin, G.; Wersäll, M.; Nilsson, S.; Antosiewicz, T. J.; Käll, M.; Shegai, T. Physical Review Letters 2015, 114, 157401. Wersäll, M.; Cuadra, J.; Antosiewicz, T. J.; Balci, S.; Shegai, T. Nano Letters 2017, 17, 551-558. Sie, E. J.; McIver, J. W.; Lee, Y.-H.; Fu, L.; Kong, J.; Gedik, N. Nat Mater 2015, 14, 290-294. He, K.; Kumar, N.; Zhao, L.; Wang, Z.; Mak, K. F.; Zhao, H.; Shan, J. Physical Review Letters 2014, 113, 026803. Liu, X.; Galfsky, T.; Sun, Z.; Xia, F.; Lin, E.-c.; Lee, Y.-H.; Kéna-Cohen, S.; Menon, V. M. Nat Photon 2015, 9, 30-34. Wang, S.; Li, S.; Chervy, T.; Shalabney, A.; Azzini, S.; Orgiu, E.; Hutchison, J. A.; Genet, C.; Samorì, P.; Ebbesen, T. W. Nano Letters 2016, 16, 4368-4374. DufferwielS; Lyons, T. P.; Solnyshkov, D. D.; Trichet, A. A. P.; WithersF; SchwarzS; MalpuechG; Smith, J. M.; Novoselov, K. S.; Skolnick, M. S.; Krizhanovskii, D. N.; Tartakovskii, A. I. Nat Photon 2017, 11, 497-501. Liu, W.; Lee, B.; Naylor, C. H.; Ee, H.-S.; Park, J.; Johnson, A. T. C.; Agarwal, R. Nano Letters 2016, 16, 1262-1269. Zhang, L.; Gogna, R.; Burg, W.; Tutuc, E.; Deng, H. Nature Communications 2018, 9, 713. Wen, J.; Wang, H.; Wang, W.; Deng, Z.; Zhuang, C.; Zhang, Y.; Liu, F.; She, J.; Chen, J.; Chen, H.; Deng, S.; Xu, N. Nano Letters 2017, 17, 4689-4697. Zheng, D.; Zhang, S.; Deng, Q.; Kang, M.; Nordlander, P.; Xu, H. Nano Letters 2017, 17, 3809-3814. Kleemann, M.-E.; Chikkaraddy, R.; Alexeev, E. M.; Kos, D.; Carnegie, C.; Deacon, W.; de Pury, A. C.; Große, C.; de Nijs, B.; Mertens, J.; Tartakovskii, A. I.; Baumberg, J. J. Nature Communications 2017, 8, 1296. Cuadra, J.; Baranov, D. G.; Wersäll, M.; Verre, R.; Antosiewicz, T. J.; Shegai, T. Nano Letters 2018, 18, 1777. Birnbaum, K. M.; Boca, A.; Miller, R.; Boozer, A. D.; Northup, T. E.; Kimble, H. J. Nature 2005, 436, 87-90. Halas, N. J.; Lal, S.; Chang, W.-S.; Link, S.; Nordlander, P. Chem. Rev. 2011, 111, 39133961. Itoh, T.; Yamamoto, Y. S.; Tamaru, H.; Biju, V.; Wakida, S.-i.; Ozaki, Y. Physical Review B 2014, 89, 195436. Santhosh, K.; Bitton, O.; Chuntonov, L.; Haran, G. Nat Commun 2016, 7, 11823. Chikkaraddy, R.; de Nijs, B.; Benz, F.; Barrow, S. J.; Scherman, O. A.; Rosta, E.; Demetriadou, A.; Fox, P.; Hess, O.; Baumberg, J. J. Nature 2016, advance online publication. Groß, H.; Hamm, J. M.; Tufarelli, T.; Hess, O.; Hecht, B. Science Advances 2018, 4.


21

Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

34. 35. 36. 37. 38. 39. 40.

41. 42.

43. 44. 45. 46. 47. 48. 49. 50.

Page 22 of 28

Qian, L.; Xiaolu, Z.; Shuang, L.; Qifeng, R.; Qing‐Hua, X.; Jianfang, W. Advanced Optical Materials 2015, 3, 801-812. Sivun, D.; Vidal, C.; Munkhbat, B.; Arnold, N.; Klar, T. A.; Hrelescu, C. Nano Letters 2016, 16, 7203-7209. Liu, M.; Guyot-Sionnest, P. The Journal of Physical Chemistry B 2005, 109, 2219222200. Liu, M.; Guyot-Sionnest, P.; Lee, T.-W.; Gray, S. K. Physical Review B 2007, 76, 235428. Gao, Y.; Liu, Z.; Sun, D.-M.; Huang, L.; Ma, L.-P.; Yin, L.-C.; Ma, T.; Zhang, Z.; Ma, X.-L.; Peng, L.-M.; Cheng, H.-M.; Ren, W. Nature Communications 2015, 6, 8569. Mak, K. F.; Lee, C.; Hone, J.; Shan, J.; Heinz, T. F. Physical Review Letters 2010, 105, 136805. Tonndorf, P.; Schmidt, R.; Böttger, P.; Zhang, X.; Börner, J.; Liebig, A.; Albrecht, M.; Kloc, C.; Gordan, O.; Zahn, D. R. T.; Michaelis de Vasconcellos, S.; Bratschitsch, R. Optics Express 2013, 21, 4908-4916. Arora, A.; Koperski, M.; Nogajewski, K.; Marcus, J.; Faugeras, C.; Potemski, M. Nanoscale 2015, 7, 10421-10429. Moody, G.; Kavir Dass, C.; Hao, K.; Chen, C.-H.; Li, L.-J.; Singh, A.; Tran, K.; Clark, G.; Xu, X.; Berghäuser, G.; Malic, E.; Knorr, A.; Li, X. Nature Communications 2015, 6, 8315. Gómez-Graña, S.; Hubert, F.; Testard, F.; Guerrero-Martínez, A.; Grillo, I.; Liz-Marzán, L. M.; Spalla, O. Langmuir 2012, 28, 1453-1459. Chen, H.; Shao, L.; Li, Q.; Wang, J. Chemical Society Reviews 2013, 42, 2679-2724. Antosiewicz, T. J.; Apell, S. P.; Shegai, T. ACS Photonics 2014, 1, 454-463. Yang, Z.-J.; Antosiewicz, T. J.; Shegai, T. Optics Express 2016, 24, 20373-20381. Sáez-Blázquez, R.; Feist, J.; Fernández-Domínguez, A. I.; García-Vidal, F. J. Optica 2017, 4, 1363-1367. Johnson, P. B.; Christy, R. W. Physical Review B 1972, 6, 4370-4379. Li, Y.; Chernikov, A.; Zhang, X.; Rigosi, A.; Hill, H. M.; van der Zande, A. M.; Chenet, D. A.; Shih, E.-M.; Hone, J.; Heinz, T. F. Physical Review B 2014, 90, 205422. Koenderink, A. F. Optics Letters 2010, 35, 4208-4210.


22

Page 23 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

ToC graphic


23

Nano Letters

Scattering (a.u.)

meV

Uncoupled System

≈ 110

γ WSe2 ≈

V

40 me

1.5

1.6

1.7

1.8

1.9

Energy (eV)

c)

d)

o

90 o

Scattering (a.u.)

Coupled System

Bipyramid WSe 2

Photoluminescence (a.u.)

b)

γ plasmon

a)

0

}N layers

.....

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 28

1.5

1.6

1.7

1.8

Energy (eV)


1.9

Page 25 of 28

Simulations

Experiment

a)

LP

b)

UP

c)

2.32

AR = 2.3

AR = 2.3

2.65

2.75

Absorption

2.61

Scattering

Normalized Scattering (a.u.)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

2.6

2.65

2.6

2.65

2.75

2.75

2.8

2.8

2.9

2.9

2.80

2.87

AR

1.4

1.6

1.8

Energy (eV)

1.4

1.6

1.8

Energy (eV)


1.4

1.6

1.8

Energy (eV)

Nano Letters

a)

1.8

1 Layer

b)

1.8

2 Layers

1.7

1.7

1.7

1.6

1.6

1.6

1.5

1.8

1.6

d)

1.7

1.8

4 Layers

1.8

1.6

e)

1.7

1.8

8 Layers

1.6

1.6

1.6

1.7

1.8

1.5

1.6

1.7

3 Layers

1.6

1.7

1.8

f)

55

90

50

80

45

1.8

Plasmon resonance (eV)


c)

1.5

100

1.7

1.7

1.5

1.5

Rabi splitting (meV)

Energy (eV)

1.8

1

2

3

4

# Layers

...

8

Coupling strength (meV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 28

3

7

2

1

30

6

1

2 3 4 5 6 7 number of WSe2 layers

8

5

0.6

b)

layer #: 1 (top)

0.5 0.4

2

0.3

3 4

0.2 0.1

5 6

1

2 3 4 5 6 7 number of WSe2 layers 30 e) 4

d)

coherent dipole moment (D)

mode volume (103 nm3)

a)

vacuum ﬁeld (×107 Vm-1)

105 100 95

90 85

8

c)

1

2 3 4 5 6 7 number of WSe2 layers

8 7 6

-10

-10

-55

-50

-45

2

5

10 y (nm)

3

10 z (nm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

maximum coupling strength to a 1 D exciton per monolayer (meV)

Page 27 of 28

4 3

-10

2

1 -30

energy density -60

-40

-20

0 x (nm)

20

1

energy density

-20

log10

40

60

-30

×103

-80


-60

-40

-20 x (nm)

0

20

Nano Letters

WSe₂

100

55

90

50

80

45

ACS Paragon Plus Environment 1

2

3

4

# Layers

...

8

Coupling strength (meV)

}

ers N lay

Rabi splitting (meV)

Au

.....

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Page 28 of 28

Strong light-matter coupling between plasmons in individual gold

Recommend Documents