Manipulating Coherent Plasmon–Exciton Interaction in a Single Silver

Letter pubs.acs.org/NanoLett

Manipulating Coherent Plasmon−Exciton Interaction in a Single Silver Nanorod on Monolayer WSe2 Di Zheng,† Shunping Zhang,*,† Qian Deng,† Meng Kang,† Peter Nordlander,†,§ and Hongxing Xu*,†,‡ †

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School of Physics and Technology, Center for Nanoscience and Nanotechnology, and Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education, ‡The Institute for Advanced Studies, Wuhan University, Wuhan 430072, China § Department of Physics and Astronomy, Department of Electrical and Computer Engineering and Laboratory for Nanophotonics, Rice University, Houston, Texas 77005, United States S Supporting Information *

ABSTRACT: Strong coupling between plasmons and excitons in nanocavities can result in the formation of hybrid plexcitonic states. Understanding the dispersion relation of plexcitons is important both for fundamental quantum science and for applications including optoelectronics and nonlinear optics devices. The conventional approach, based on statistics over different nanocavities, suffers from large inhomogeneities from the samples, owing to the nonuniformity of nanocavities and the lack of control over the locations and orientations of the excitons. Here we report the first measurement of the dispersion relationship of plexcitons in an individual nanocavity. Using a single silver nanorod as a Fabry-Pérot nanocavity, we realize strong coupling of plasmon in single nanocavity with excitons in a single atomic layer of tungsten diselenide. The plexciton dispersion is measured by in situ redshifting the plasmon energy via successive deposition of a dielectric layer. Room-temperature formation of plexcitons with Rabi splittings as large as 49.5 meV is observed. The realization of strong plasmon−exciton coupling by in situ tuning of the plasmon provides a novel route for the manipulation of excitons in semiconductors. KEYWORDS: Strong coupling, plexciton, exciton, plasmonics, nanocavity, transition metal dichacogenides where λ is the wavelength of light in the medium) of a cavity photon cannot be further compressed due to the diffraction limit. Metallic nanocavities that sustain surface plasmons (SPs) with subwavelength mode confinement serve as an alternative candidate for realizing strong plasmon-exciton (“plexciton”) coupling. Recent studies have successfully demonstrated strong plasmon−exciton coupling at the single nanoparticle level, using J-aggregates,8−10 quantum dots,11 or molecules12 down to single exciton level. However, deterministic spatial and spectral coincidences between the plasmonic nanocavity and the exciton transition dipole in these systems represent a significant technical challenge. One reason stems from the fact that the plasmon resonances are fixed once the nanocavity is fabricated. Another reason is that the spatial distribution of the excitons and their orientations with respect to the electric field around the nanocavities is hard to control. These two challenges have hampered the realization of strong coupling and, in particular, have prevented the measurement of the dispersion relation of plexcitons on an individual nanoparticle. Instead, plexciton dispersion measurements have had to rely on fabrication of

T

he ability to couple electronic transitions to photonic or plasmonic resonances in cavities has inspired several interesting studies on light−matter interaction at the nanoscale. When the coherent energy exchange rate between a cavity photon and an electronic transition is sufficiently fast compared with their energy dissipation or decoherence rate, the system is in the strong coupling regime, resulting in hybrid states that are part-light and part-matter. Exciton−polaritons in microcavities can serve as excellent platforms to study fundamental quantum science such as entanglement1 and Bose−Einstein condensation2 and to control several phenomena such as spontaneous emission, stimulated emission and Förster energy transfer. Such fundamental processes also play an important role in applications such as low-threshold lasers,3 enhanced exciton conductance,4,5 and strong optical nonlinearity.6,7 The realization of strong coupling relies on increasing the coupling strength while reducing the dissipation and decoherence rates. The coupling strength is proportional to the inner product of the exciton transition dipole moment μ and the electric field E of the cavity photons. The ability of a passive cavity to realize strong coupling can be characterized by the ratio of the quality factor (Q) to the cavity mode volume V. Usually, a high Q on the order of 106 are required in photonic cavity systems because the mode volume (on the order of λ3, © 2017 American Chemical Society

Received: March 20, 2017 Revised: May 13, 2017 Published: May 22, 2017 3809

DOI: 10.1021/acs.nanolett.7b01176 Nano Lett. 2017, 17, 3809−3814

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Nano Letters

Figure 1. Optical properties of the uncoupled constituents. (a) A schematic of the system with a single silver nanorod on a monolayer WSe2. (b) Electromagnetic calculations of the near-field distribution of the n = 3 silver nanorod plasmon mode (diameter 24 nm, length 282 nm). (c) A representative dark-field scattering spectrum of an uncoupled silver nanorod and the photoluminescence spectrum of a single layer WSe2. The inset shows the scanning electronic microscopy image of the corresponding silver nanorod.

in a single atomic layer.17−20 Similar to other TMDs at the single layer limit, it becomes a direct band gap material with a large transition dipole moment μ that can couple strongly to the light.13,14,21−26 The reduced dielectric screening and the quantum confinement in the 2D limit give rise to the exceptionally large binding energies compared to traditional semiconductors.17 This large binding energy makes the excitons insensitive to thermal excitations, thus allowing strong exciton− light coupling under ambient condition. Superior to other excitonic materials like molecules or colloidal quantum dots whose positions and orientations are hard to control, the choice of monolayer TMDs also benefits from a relatively homogeneous spatial distribution and well-defined in-plane orientated transition dipoles27,28 that are essential for quantitative analysis. Monolayer WSe2 samples were mechanically exfoliated onto a Si substrate with 444 nm thermally grown SiO2. CCD contrast was used to identify the monolayer WSe2, and photoluminescence, Raman, and atomic force microscope (AFM) measurements were carried out to confirm the monolayer nature (see SI Figure S2). An alumina layer of 3.2 nm was deposited onto the WSe2 to prevent direct contact to the nanoparticle, eliminating possible charge transfer processes.29,30 Uniform silver nanorods were synthesized in high throughput by a gold nanobipyramid-directed method.31 The diameters of the silver nanorods are controlled by the width of the gold nanobipyramids, while their lengths can be adjusted by changing the reaction time. Since both gold and silver are good plasmonic materials at visible frequencies, the SP propagates without significant reflections at the gold and silver interfaces. The overall resonances show clear Fabry-Pérot type dispersion similar to those in pure silver nanorods, but with a slight redshift due to the smaller SP resonant frequency of gold. Single particle dark-field spectroscopy was used to measure the scattering spectra of the individual nanorods, followed by a correlated scanning electronic microscopy (SEM) characterization of their morphologies. Nonpolarized white light from a halogen lamp (100 W, Olympus) was obliquely illuminated on the sample with an angle of 80° with respect to the substrate normal. The scattered light was collected by an Olympus

different nanocavities with different plasmon energies where the uncertainties associated with sample inhomogeneities is significant.8−10,12 In this study, we realize strong coupling of SP on an individual nanorod with excitons in a monolayer tungsten diselenide, one type of transition metal dichacogenides (TMDs) that is promising for optical and optoelectronic applications. Deterministic spectral coincidence is achieved by successively tuning the energy of the SP by depositing a thin dielectric layer onto the nanorod. Deterministic spatial coincidence is accomplished by the near-field interaction between the in-plane 2D Wannier type excitons and the nanorod plasmon. The dispersion curves of the hybrid plexcitonic states are mapped out in situ giving a definite plasmon-exciton Rabi splitting of 49.5 meV, free of any uncertainty associated with the inhomogeneities of different samples. Furthermore, the use of excitons in a single atomic layer crystalline material instead of in organic molecules or their aggregates, represents an important step toward developing integratable optoelectronic devices. Strong plasmon−exciton coupling has been realized between plasmonic lattice and TMDs,13,14 but to the best of our knowledge, our study is the first to realize strong plasmon-exciton coupling on single layer TMDs with individual metallic nanoparticles. Our plexciton system is fabricated by simply dropping cast and spinning a metal nanorod onto a monolayer WSe2 (Figure 1a). More fabrication details can be found in Supporting Information (SI) S1. We chose silver nanorod since it behaves like a nanometric Fabry-Pérot cavity for the axisymmetric SP on 1D nanowire.15 Resonant modes are formed when the propagating SP accumulates a 2nπ phase during a round trip between the two ends. Modes of different orders, indexed by the number of nodes n along the nanorod axis, can be clearly identified in the spectrum since their resonant energies depend linearly on the length of the nanorod (see SI, Figure S3c). Specifically, we choose the n = 3 mode as shown in Figure 1b. It satisfies the high-Q−low-V criterion in that its Q is about three times higher than for the dipolar plasmon resonance (n = 1) on the nanorod.16 WSe2 was chosen due to its giant excitonic effect 3810

DOI: 10.1021/acs.nanolett.7b01176 Nano Lett. 2017, 17, 3809−3814

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Figure 2. Strong coupling of nanorod SP and WSe2 excitons. (a−c) Bright-field image, dark-field image, and SEM image of the silver nanorod on bare substrate. (d−f) Bright field image, dark-field image, and SEM image of the silver nanorod on monolayer WSe2. (g) A set of dark-field scattering spectra of the silver nanorod correspond to a−c with increased alumina coating. (h) A set of dark-field scattering spectra of the silver nanorod correspond to d−f with an increased alumina coating.

using atomic layer deposition. Uniform alumina coating can be coated over the entire surface of the sample, with its thickness precisely controlled and finally calibrated by the reaction circles (see SI S1 for more details). Since the refractive index of the alumina is larger than that of the air, the SP energy will gradually redshift due to dielectric screening effect,34 a feature that has been widely used for chemical or biological sensing. Similar techniques have been used to tune the resonant frequencies in photonic cavities by gas adsorption.35,36 For a nanorod on substrate without WSe2 (Figure 2a−c), the plasmon resonance red-shifted from 646 to 735 nm as the coating thickness increases from 3.2 to 38 nm (Figure 2g). The shift per unit coating is larger at the beginning and become smaller when the coating is thick and follows an exponential decay as the coating thickness increases (Figure S6c). This shift reflects the attenuation of the SP near-field away from the metal surface. Alumina is a transparent dielectric that has little effect on the X0 exciton in WSe2 (Figure S7). Therefore, tuning the SP energy is an efficient way of varying plasmon−exciton detuning. As the SP energy Epl shifts across the exciton E0, clear evidence of strong couplingspectral splittingis manifest in the scattering spectra (Figure 2h). The overall redshift of about 37 nm between the two groups of scattering spectra is due to slightly different geometries of the nanorods and a larger permittivity of the WSe2 layer compared to that of the silicon oxide substrate. Also, the resonant peaks in Figure 2h are slightly broader than those in Figure 2g, because of the absorption in WSe2. The plasmon−exciton coupling can be described by the quantum mechanical Jaynes−Cummings model. However, if the number of excitons involved is large, quantum statistical effects only play a small role, and a simpler coupled oscillator model (COM) can provide an accurate physical picture as well. The collective response of the excitons can then be viewed as a “super oscillator”, and the system can be qualitatively modeled as two coupled harmonic oscillators:37

objective (100X, N.A. = 0.8) and then directed to a spectrometer (Renishaw inVia), see SI S3 for more details on dark field measurement. A background spectrum taken from a nearby area was subtracted from each measured silver nanorod spectrum. We choose a nanorod whose length is around 280 nm with the desired n = 3 mode on the blue side but close to the neutral (X0) exciton in monolayer WSe2. A representative dark-field scattering spectrum in Figure 1c shows the peak width of the n = 3 mode is as small as 57 meV, and the exciton width is Γ0 = 38 meV (measured by photoluminescence in Figure 1c) or 43 meV (measured by absorption in Figure S9). The narrow plasmon peak width is due to the high reflectivity of SP at the nanorod ends as a result of the large momentum mismatch between the SP and free space photons.32 Such sharp plasmon peaks are crucial for realizing strong plasmon-exciton coupling. The Q factor reaches as high as 32, meaning that the plasmon survives on the nanorod for 32 cycles before dephasing. Therefore, the local field E gets significantly enhanced compared to the electric field of a photon in vacuum. As confirmed by electromagnetic calculations in Figure 1b, the maximum field enhancement in the close vicinity of the nanorod reaches 35, which will enhance the coupling of the plasmon to excitons. The asymmetric line shape of the n = 3 resonance mode is due to the Fano interference between the n = 3 with the n = 1 nanorod plasmon.16,33 The broad peak around 780 nm does not influence the coupling between the n = 3 mode and the excitons and is associated with the nanorod sample (more discussion see SI S2). The realization of strong plasmon−exciton coupling requires simultaneous spectral and spatial overlap. The spatial coincidence is accompanied by dropping the nanorods onto the two-dimensional sheet of WSe2. Thus, the confined excitons are automatically brought into the near-field region of the plasmon, with their transition dipole moments interacting with the in-plane components of the SP. The spectral coincidence is accomplished by continuously redshifting the plasmon resonance across the excitonic transition via successive deposition of alumina layers onto the sample 3811

DOI: 10.1021/acs.nanolett.7b01176 Nano Lett. 2017, 17, 3809−3814

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Figure 3. Dispersion of plexciton. (a) The energy of the UPB (E+, blue square) and LPB (E−, magenta triangle) as a function of detuning. The solid lines are fit to the COM eq 1, giving a splitting of 49.5 meV. The extracted energy of the plasmon (Epl, gray dot) is included for comparison. The gray dashed lines are guide to the eyes showing the dispersion of the uncoupled exciton and plasmon. (b) Coupling strength g as a function of alumina thickness. (c, d) Hopfield coefficients for the UPB (c) and LPB (d), calculated from eq 1.

Figure 4. Calculated scattering spectra for a single nanorod with different coating. (a) Without WSe2; (b) With WSe2 (diameter 25 nm, length 284 nm). (c, d) The x and y components of the plasmon near field normalized to the energy of half a single plasmon quantum Epl. (e) Color contour map of the plasmon−exciton coupling.

⎛ Epl − i Γpl /2 ⎞⎛ α ⎞ g ⎛α ⎞ ⎜ ⎟⎜ ⎟ = E ⎜ ⎟ ⎜ ⎟⎝ β ⎠ ⎝ β⎠ g E0 − i Γ0/2 ⎠ ⎝

determined from the X0 absorption peak in Figure S9). The energy of the upper plexciton branches (UPB) and lower plexciton branches (LPB) exhibits a clear anticrossing behavior (Figure 3a). A vacuum Rabi splitting of Ω = 2g|δ=0 = 49.5 meV is obtained at zero detuning. It is larger than the peak width of the exciton (43 meV) and smaller than the peak width of the uncoupled nanorod plasmon (98 meV). Although it does not rigorously satisfy the criteria for strong coupling (Ω > (Γpl + Γ0)/2), it is close. The fitting of the coupling strength g as a function of alumina thickness shows a maximum variation of 3% (Figure 3b), which is much smaller than those obtained by statistics over different samples. Our approach therefore represents a significant advantage over the conventional schemes for measuring plexciton dispersion relations. The small variation of g in Figure 3b is mainly caused by the fitting procedure. Moreover, conventional plexcitonic systems suffer from low yield due to the lack of control over the exciton positions and orientations. Our approach of constructing plexciton system gets rid of this draw back thank to the uniformity of the nanorod samples and the dielectric coating scheme (see Figure S8 for another example). The fraction of

(1)

where Epl and E0 is the energy of the nanorod plasmon and the X0 excitons, and g is the coupling strength. Γpl and Γ0 denote the dissipation rates. E are the eigenvalues corresponding to the energies of the new quasiparticles (plexcitons) and α and β, are the eigenvector components (Hopfield coefficients) and satisfy |α|2 + |β|2 = 1. The eigenvalues E are obtained from the secular equation ⎛ ⎞⎛ ⎞ 1 1 ⎜E − i Γpl − E⎟⎜E0 − i Γ0 − E⎟ = g 2 pl ⎝ ⎠⎝ ⎠ 2 2

(2)

When the widths of the plasmon and exciton are small compared to their energies, the energy of plexcitons can be 1

approximated as E± = 2 (Epl + E0) ±

1

g 2 + 4 δ 2 , where δ =

Epl − E0 is the detuning. By fitting the scattering spectra in Figure 2h to the COM model (see SI, Figure S6b), we extracted Epl and g (assuming E0 = 1.659 eV which was 3812

DOI: 10.1021/acs.nanolett.7b01176 Nano Lett. 2017, 17, 3809−3814

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measured value if we assume η = 0.75. Such η < 1 means that the density of WSe2 excitons is slightly smaller when the nanorod is present than for the bare substrate from which the WSe2 absorption is taken. This is most likely because of the reduction of the transition dipole moment for finite k away from the K valley,40 since plasmons in the Fabry-Pérot nanocavity propagate parallel to the WSe2 sheet while light travels perpendicular to the WSe2 sheet in absorption measurement. Another possibility is the parasitic light absorption in the nanorod. A more precise theory describing the light−matter interaction beyond the dipole approximation is required to account for the mesoscopic nature of the excitons. Using the above-mentioned exciton density, our experiments suggests that the plexciton state involve Ne = 4100 excitons. Since the plexciton system was probed by dark-field scattering in which the excitation power was quite low, the system is in the linear region. Therefore, the coupling strength g as well as the evaluated exciton number is not affected by the excitation power. This correlated state may have properties that could be exploited in applications such as exciton transport. For example, energy exchange between different excitonscreation of an exciton at one position via annihilating another exciton far apartcan be accelerated since they interact through the plasmon. Compared to exciton transport by hopping, plexcitons can bypass local atomic disorder and significantly improve the exciton conductance due to their hybrid delocalized plasmonic characteristics.4 In conclusion, we have developed an approach for measuring the dispersion relation of plexcitons in an individual hybrid nanocavity consisting of a silver nanorod on a WSe2 monolayer. The dispersion relation is measured by in situ red shifting the nanorod plasmon energy via successive deposition of alumina. Our measured Rabi splitting suggests that the system is close to the strong coupling regime and involves many excitons interacting through the plasmon. Exploiting the tunability of SPs when coupled to the excitons provides a new opportunity to modify the properties of plexcitons (“dressed” excitons) that would be useful for many optoelectronic applications. The flexible “sheet” nature of monolayer TMDs also enables its integratability with different substrates and the development of plexcitonic devices.

plasmon and exciton constituents in the UPB and LPB can also be obtained from the COM (Figure 3c,d). Since the detuning changes from positive to negative, the plasmon (exciton) constituent dominates UPB (LPB) for small dielectric coating and reverses for large coating thickness. The optical properties of the nanocavity−monolayer WSe2 structure were modeled using full wave finite element simulations (COMSOL Mutiphysics 5.2, Wave optics module) with structural and optical coefficients appropriate for the fabricated system. The permittivity of gold and silver were taken from Johnson and Christy.38 The refractive index of alumina is taken as 1.5, which reproduced the redshift behavior of the nanorod on bare substrate. The thickness of WSe2 layer was taken to be 0.7 nm. The permittivity of the WSe2 is anisotropic with the in-plane components modeled as a Lorentz oscillator: εWSe2(E) = ε∞ − f

E0 2 E2 − E0 2 + iE Γ0

(3)

where ε∞ accounts for the high frequency contribution to the permittivity, and f is the reduced oscillator strength of the exciton. E0 and Γ0 are taken from the absorption spectra of WSe2 layer on silica substrate. The out-of-plane permittivity was assumed to be a constant εout = 2.9, taken from ref 39. The nanorod was modeled with a diameter of 25 nm and a length of 284 nm. The gold bipyramid core inside the silver nanorod was modeled as a spheroid with the long axis 39 nm and the diameter 22.5 nm. The calculated and measured scattering spectra agree very well (Figure 4a,b). To evaluate the exciton−plasmon coupling strength, we calculate the plasmon induced near-field around the nanocavity without the excitons. Briefly, the energy density of scattered field was integrated and normalized to half of a single plasmon quantum Epl. Since excitons in TMDs are known to be in-plane, the in-plane components Eip of the normalized electric field within the WSe2 layer were calculated (Figure 4c,d). Although smaller than the out-of-plane component, |Eip| becomes as high as 3.5 × 106 V/m, which is 18 times larger than the electric field of a photon within a λ3 volume. This enhancement is due to the significant subwavelength confinement induced by the nanocavity plasmon. The transition dipole moment of the X0 2D Wannier exciton, |μ| = 7.675 D, is determined from its absorption spectra (SI S5). Since the exciton radius is small a = 1 nm, the coupling is local and can be evaluated as g(r) = μ· Eip(r), where r is the position of the exciton. Those excitons located right under the center of the nanorod couple strongest with the plasmon, at a rate of 0.55 meV. However, this value is much smaller than the measured Rabi splitting of 49.5 meV, suggesting that multiple excitons are involved. To evaluate the number of excitons Ne that contribute to the plexciton, we assume that the excitons are distributed uniformly in the central plane of the WSe2 layer with a density defined by ne = η/πa2, where η is a unitless parameter characterizing the overlapping of the excitons and a the exciton radius. According to the definition of exciton radius, η equals unity in bare WSe2 layer. If collective effects such as superfluorescence are neglected, the effective coupling strength between the plasmon

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.7b01176. Detailed description of the sample fabrication and characterization, dark-field scattering microspectroscopy, scattering spectra analysis, monolayer WSe2 X0 exciton transition dipole moment evaluation, and exciton number evaluation (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Phone: +8627 68752219. *E-mail: [email protected]. Phone: +8627 68752253.

2

and the ensemble of excitons becomes g = ∑i g (ri) , where g(ri) = μ·Eip(ri) is the coupling strength for the i-th exciton at position ri, as shown in Figure 4e. After summing over the contributions from individual excitons close to the nanocavity (see SI S7), we find that g will saturate to the experimental

ORCID

Shunping Zhang: 0000-0002-8491-0903 Peter Nordlander: 0000-0002-1633-2937 3813

DOI: 10.1021/acs.nanolett.7b01176 Nano Lett. 2017, 17, 3809−3814

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S.P.Z. conceived the idea. D.Z. and Q.D. prepared the samples and performed the experiments. S.P.Z. and M.K. performed theoretical simulations. D.Z., S.P.Z., and H.X.X. analyzed the data. S.P.Z., D.Z., P.N., and H.X.X. wrote the paper. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Rachel Lee Siew Tanb and Prof. Hongyu Chen for the preparation of the silver nanorods and Xiaoguang Li and Pengfei Suo for helpful discussions. This work was supported by the Ministry of Science and Technology (Grant No. 2015CB932400), the National Natural Science Foundation of China (Grants Nos. 11304233, 11134013, and 11227407), and the China Postdoctoral Science Foundation (Grant No. 2014T70727).

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DOI: 10.1021/acs.nanolett.7b01176 Nano Lett. 2017, 17, 3809−3814