Observation of tunable charged exciton polaritons ... - ACS Publications

Letter Cite This: Nano Lett. 2018, 18, 1777−1785

pubs.acs.org/NanoLett

Observation of Tunable Charged Exciton Polaritons in Hybrid Monolayer WS2−Plasmonic Nanoantenna System Jorge Cuadra,*,† Denis G. Baranov,† Martin Wersal̈ l,† Ruggero Verre,† Tomasz J. Antosiewicz,†,‡ and Timur Shegai*,† †

Department of Physics, Chalmers University of Technology, 412 96, Göteborg, Sweden Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland

‡

S Supporting Information *

ABSTRACT: Formation of dressed light-matter states in optical structures, manifested as Rabi splitting of the eigen energies of a coupled system, is one of the key effects in quantum optics. In pursuing this regime with semiconductors, light is usually made to interact with excitons, electrically neutral quasiparticles of semiconductors; meanwhile interactions with charged threeparticle states, trions, have received little attention. Here, we report on strong interaction between localized surface plasmons in silver nanoprisms and excitons and trions in monolayer tungsten disulfide (WS2). We show that the plasmon−exciton interactions in this system can be efficiently tuned by controlling the charged versus neutral exciton contribution to the coupling process. In particular, we show that a stable trion state emerges and couples efficiently to the plasmon resonance at low temperature by forming three bright intermixed plasmon−exciton−trion polariton states. Our findings open up a possibility to exploit electrically charged polaritons at the single nanoparticle level. KEYWORDS: Strong coupling, exciton, trion, TMDC, monolayer WS2

I

arrays.22,23 At the single plasmonic nanoantenna level, strong coupling has been recently demonstrated at room temperature between excitons in WS2 and Au nanorods24 and WSe2 and Ag nanorods.25 Photoluminescence (PL) can also be affected by coupling to plasmonic nanoantennas. Indeed, enhancement as well as modification of PL signal has been reported in various realizations in the weak coupling regime.26−31 Importantly, monolayer TMDCs are chemically inert, stable, and robust at ambient conditions, what makes them advantageous for active and nonlinear plasmonics applications.32 Such active control has been demonstrated in various hybrid nanostructures, including controllable and reversible switching of the strong coupling regime in microcavities loaded with photochromic molecules,33 silver nanoparticle arrays under UV illumination,34 ultrafast tuning of strongly coupled metalmolecular aggregates via femtosecond pumping,35,36 electrostatic gating and temperature control,37 and dynamical modification of the polariton composition.38 Demonstrations of thermalization, cooling, and lasing of plasmon−exciton polaritons have been reported recently.39−41 However, in these works reversible switching was demonstrated in the systems that involved only electrically neutral excitations.

nteraction between light and matter is at the heart of modern optics. It is present in atomic physics as well as in solid-state systems and plays an essential role in cavity quantum electrodynamics (cQED). When the rate of energy exchange between photons and matter excitations becomes faster than the decoherence rates of both subsystems, a special regime of light-matter interactions called strong coupling is achieved.1−5 Under these conditions formation of polaritons, which are hybrid states possessing both light and matter character, is observed. Recently, it has been shown that metallic nanoparticles enable this nonperturbative regime of light-matter interaction due to a combination of deeply subwavelength confinement of electromagnetic radiation with large transition dipole moments of molecular excitons.6−8 Monolayers of transition metal dichalcogenides (TMDC) are semiconductor materials with a direct band gap transition9 and exceptionally high optical absorption reaching values of 10% for MoS2 and as much as 15% for WS2 at resonance.10,11 The high absorptivity of TMDC monolayers makes them ideal candidates for realization of the strong coupling regime. Importantly, TMDCs support both neutral (X) and charged (T) exciton resonances.12−14 Additionally, the large spin−orbit coupling in these materials permits a spin-valley degree of freedom accessible by optical dichroism15,16 and opens routes for exploring valley polaritons.17,18 Observations of strong coupling between TMDCs and nanophotonic resonators have been reported in various systems including optical microcavities19−21 and diffractive modes of plasmonic nanoparticle © 2018 American Chemical Society

Received: November 24, 2017 Revised: January 17, 2018 Published: January 25, 2018 1777

DOI: 10.1021/acs.nanolett.7b04965 Nano Lett. 2018, 18, 1777−1785

Letter

Nano Letters Conversely, relatively little attention has been devoted to strong coupling with charged excitons. Such interactions would result in the formation of exciton polaritons carrying a nonzero net electrical charge and thus open routes to manipulate light with electricity and vice versa. Several works report observation of charged polaritons in microcavities loaded with quantum wells at low temperature,42−44 charged quantum dots,45 tunable polaron polaritons21 and MoSe2 monolayers in microcavities.17 Electrostatic gating of a MoS2 monolayer coupled with a plasmonic diffractive array also showed signatures of charged excitons being involved in the coupling, although strong coupling with trions was not reported.46 Electro-optical control of trions in the Fano regime was also demonstrated very recently.47 The existence of charged exciton polaritons opens a number of intriguing perspectives, as such quasiparticles are anticipated to strongly interact with each other and to improve charge and exciton transport properties mediated by strong coupling.44,48 Here, we demonstrate strong interactions between plasmons in an individual silver nanoprism and neutral as well as charged excitons in monolayer WS2. The latter is especially interesting, as this opens up a new way to control and manipulate charge via light-matter interactions and vice versa. In this study, we show that the degree of plasmon−exciton−trion coupling can be tailored by temperature. In particular, by tuning the temperature in the wide range between 6 and 300 K, we are able to observe a transition from two polaritonic resonances at room temperature, corresponding to plasmon−exciton interaction, to the formation of three polaritonic resonances at T = 6 K, corresponding to three body intermixed plasmon− exciton−trion polaritons. Results. System under Study. The coupled system in this work is composed of colloidal silver nanoprisms positioned on top of a WS2 monolayer. We start by preparing the monolayer by mechanical exfoliation from a high quality crystal and transferring it to a thermally oxidized silicon substrate. The monolayer nature of the WS2 flake, which can readily reach sizes greater than ∼100 μm (see Figure 1a), is confirmed by optical contrast and a bright PL signal−typical for direct bandgap semiconductors (Figure 1b). The PL spectrum at 300 K under ambient conditions shows maximum at 2.012 eV (ωX) and corresponds to the neutral A-exciton with a binding energy of about 700 meV.49 The PL signal at 200 and 77 K in contrast to the room temperature data exhibits two peaks: the high-energy resonance (2.07 eV) and the low-energy peak (2.03 eV). We assign the former to the neutral A-exciton, which undergoes a blue shift, whereas the latter corresponds to the positively charged exciton (ωT), a trion. Upon further cooling to T = 6 K several additional peaks are observed in the PL spectrum, the two peaks at high energy being the exciton and trion, whereas the additional peaks may arise due to bound excitons, which become stable at low temperature.50,51 The trion state dominates the PL at low temperatures and has a binding (or dissociation) energy of about 40 meV in agreement with earlier reports.49 The trion state is likely positively charged because of the high density of electron acceptors in the polymer layer used in this study to facilitate binding of plasmonic nanostructures (see Methods and Figure S3). For comparison, in the Supporting Information (SI) we show reflectivity and PL data for the WS2 without the p-doped polymer layer. We note that in recent studies on field effect transistors incorporating WS2, trions of both positive and negative polarities and dissociation energies, which depend on

Figure 1. Hybrid 2D material−nanoparticle plasmon system. (a) Bright-field optical image of the exfoliated WS2 flake. Monolayer regions are marked by the dotted line (scale bar 50 μm). (b) PL spectra of the WS2 as a function of temperature. The red curve shows the PL taken at room temperature. The resonance at 616 nm corresponds to the neutral A-exciton (X), while the trion (T) peak is absent. The blue curve shows the PL at T = 6 K. The peak at 598 nm is the neutral A-exciton that blue shifts at low temperature. The peak at 611 nm is the trion and dominates the PL emission. At intermediate temperatures, T = 200 K and T = 77 K, PL spectra show both X and T peaks, whose resonance position and relative intensity depend on the temperature. (c) DF microscope image of the WS2 flake covered with silver nanoprisms. Monolayer regions are marked by the red dotted line (scale bar 50 μm). (d) Artist view of the hybrid system: high density of photonic states (hot-spots) is shown at the corners of the nanoprism, which overlaps with the WS2 monolayer for efficient plasmon−exciton interaction. Inset shows the SEM image of such a particle (scale bar 100 nm) and a magnified view of a corresponding DF image.

the applied gate voltage, were reported.52 Similarly, positive trions arising from a charge transfer process were observed in van der Waals WS2/MoS2 heterostructures.53 The latter effect is analogous to the one caused by the p-doped polymer layer in the present work. We also note that the trion states were previously reported to be stabilized by molecular doping.54 The second ingredient to construct the hybrid system in this study is the silver nanoprism (see Figure 1d). These nanoparticles were prepared by a seed-mediated colloidal synthesis and are single crystalline in nature, which greatly improves the quality factor of the plasmon resonance and thus its coupling to the 2D material.55 A typical nanoprism has dimensions of about 60−80 nm in side length and about 10 nm in thickness. Such nanoprism dimensions result in a plasmon resonance, ωpl, overlapping with the exciton transition, ωX, in monolayer WS2. Thus, by combining these two materials one could expect strong plasmon−exciton interactions. In order to verify this expectation, we positioned Ag nanoprisms on top of the WS2 monolayer by drop casting a nanoparticle suspension on a polymer precoated substrate (see Methods). As a result we obtain a monolayer WS2 flake covered with Ag nanoprisms of various sizes as is evidenced by the dark-field (DF) optical microscopy (see Figure 1c). The colorful spots in the image are individual Ag nanoprisms (confirmed by SEM measurements) possessing different plasmon resonances. Such configuration allows us to study a variety of plasmon−exciton resonance detunings δ = ωpl − ωX within the same sample. A combined 2D material−silver nanoprism system is depicted schematically 1778


Letter

Nano Letters in Figure 1d. The regions of maximal electric field enhancement around the nanoprism are localized at the corners of the prism and are shown schematically by the bright spots. Insets show a magnified DF image of a single nanoprism and an SEM image of the coupled system. The latter confirms that an individual nanoprism is measured in the optical microscope. Temperature Evolution of the Coupled System. We now explore the evolution of the strongly coupled system by varying its temperature (see Methods for experimental details). Because the PL spectrum exhibits the appearance of an additional trion resonance at low temperatures, one could expect involvement of this additional resonance into the plasmon−exciton coupling process. The temperature evolution of the DF spectra of the coupled system is shown in Figure 2. SEM confirms that the

both exciton and trion resonances with the plasmonic cavity can occur, because the plasmon line width is typically much broader than the exciton−trion spectral detuning. The hybrid system thus experiences a transition from plasmon−exciton interactions at room temperature to more complex plasmon− exciton−trion interactions at low temperatures, which is schematically illustrated in Figure 2 (right panel). To shed more light on the nature of the coupled states, we perform DF scattering measurements for nanoparticles of several different sizes and therefore plasmonic resonances. These experiments in turn allow to extract the anticrossing relations characterizing the strong coupling regime of interaction. Hamiltonian Analysis and Anticrossing. Depending on the temperature, the hybrid system can be described by plasmon− exciton or plasmon−exciton−trion interactions. To describe these interactions we use a matrix representation of a corresponding Hamiltonian (see eq 1). We choose to analyze T = 6 and 300 K temperature points in depth, as these temperatures represent the most extreme coupling scenarios in this study. The intermediate temperature points can be considered as a smooth transition between these two extremes. The composition of the hybrid states can be modeled by diagonalizing the Hamiltonian of the coupled system

Figure 2. Coupled system at various temperatures. Left: Dark-field scattering spectra at T = 300, 200, 77, and 6 K. At room temperature the DF spectrum depicts two peaks, namely the upper and lower polaritons. At lower temperatures the DF spectrum shows three peaks that are identified as upper, middle, and lower polaritons. Arrows represent the splitting caused by excitons at 300 K whereas the splitting is caused by excitons and trions at 6 K. (Inset: SEM image of the corresponding individual Ag nanoprism. Scale bar = 100 nm). Right: Artist view of plasmon−exciton mixture at T = 300 K and plasmon−exciton−trion interaction at T = 6 K.

γpl ⎛ ⎞ gX ⎜ ωpl − i ⎟ 2 ⎟ /̂ = ℏ⎜ ⎜ γX ⎟ ⎜ gX ωX − i ⎟ ⎝ 2⎠

(1a)

γpl ⎛ ⎞ gX gT ⎟ ⎜ ωpl − i 2 ⎜ ⎟ ⎜ ⎟ γ /̂ = ℏ⎜ gX ωX − i X 0 ⎟ 2 ⎜ ⎟ γT ⎟ ⎜ ⎜ 0 gT ωT − i ⎟ ⎝ 2⎠

(1b)

where γpl, γX, and γT are the widths of the plasmon, exciton, and trion, respectively, while gX and gT are the plasmon−exciton and plasmon−trion interaction constants, respectively. At room temperature, we adopt eq 1a, while at 6 K we use eq 1b. Note that we assume no direct coupling between excitons and trions and any interaction between them is mediated by the plasmon. The diagonalization of these Hamiltonians yields new polaritonic eigenfrequencies and Hopfield coefficients, which represent the contribution of plasmons, excitons, and trions to each polariton state.57 To perform the analysis, we first obtain the corresponding eigenfrequencies for the upper − ωUP, middle − ωMP, and lower − ωLP polaritons (or ωUP, ωLP for the room temperature), from experimental DF data. Since ωX and ωT are known from independent PL and/or reflectivity measurements, we obtain the unknown ωpl from the equalities that connect the hybrid eigenfrequencies with the original uncoupled ones: ωUP + ωMP + ωLP = ωpl + ωX + ωT (or ωUP + ωLP = ωpl + ωX). These equalities naturally follow from trace invariance of the matrix representation of the Hamiltonian. We plot the dispersion (or anticrossing) curves obtained by measuring several different plasmonic nanoantennas of slightly different plasmon resonance frequencies. The experimental anticrossing curves are then fitted with polariton eigenfrequencies, extracted using the corresponding Hamiltonian model.

system is an individual Ag nanoprism (inset Figure 2). At room temperature, scattering reveals the splitting of the resonance into two peaks, which, as will be demonstrated later, arises from strong plasmon−exciton coupling, that is the formation of polaritons. By cooling the system, the trion contribution to the PL spectrum starts to emerge due to oscillator strength redistribution between the exciton and trion resonances. This redistribution in turn affects the coupling between the plasmonic nanoprism and the 2D material, which we monitor via the DF spectroscopy. We observe an emergence of two dips in the DF spectra as the temperature is reduced (Figure 2). Upon cooling to liquid nitrogen (77 K) and liquid helium (6 K) temperatures, the trion state becomes more and more pronounced in both PL and DF spectra. Cooling is also accompanied by a blue shift of both exciton and trion resonances. This behavior is consistent with the standard semiconductor behavior under low temperatures (see SI and Figure S5). It is also worth noting that at T = 6 K we do not observe any signature of interaction between localized/bound states and the plasmonic cavity, likely due to the insignificant oscillator strength these states possess.56 As exciton and trion resonances are spectrally detuned by only ∼40 meV with respect to each other, the interaction of 1779


Letter

Nano Letters

Figure 3. Anticrossing behavior of the coupled system. (a) Left: Red and blue circles represent experimental upper and lower polariton (UP and LP) eigen energies as a function of plasmon resonance position extracted from dark-field spectra of individual silver nanoprism−monolayer WS2 hybrids of various sizes and plasmon−exciton detuning at T = 300 K. Solid red and blue lines represent the eigen energies extracted from the Hamiltonian analysis eq 1a. Black solid lines indicate exciton and plasmon resonances. Right: Hopfield coefficients for plasmon and exciton contributions to UP and LP states as a function of plasmon resonance. (b) Left: Red, green, and blue circles represent experimental UP, MP (middle polariton), and LP eigen energies as a function of plasmon resonance position extracted from dark-field spectra of individual silver nanoprism−monolayer WS2 hybrids of various sizes and plasmon−exciton−trion detuning at T = 6 K. Solid red, green, and blue lines represent the eigen energies extracted from the Hamiltonian analysis eq 1b. Black solid lines indicate exciton, trion, and plasmon resonances. Right: Hopfield coefficients for plasmon, exciton, and trion contributions to UP, MP, and LP states as a function of plasmon resonance.

eigenfrequencies. As a consequence, no simple criteria for the strong coupling in this case apply. We therefore rely on fitting the experimental data with eq 1b in order to extract the parameters of the coupled system. On the basis of the fitting, the minimal splitting between the upper and lower polariton branches is around ΩUP−LP ≈ 150 meV, which is about 30 meV larger than the Rabi splitting at room temperature. Such an increase can be explained by the fact that exciton and trion are detuned with respect to each other by ∼40 meV. At the same time, both plasmon and exciton resonances are narrowed upon cooling. Exciton line narrowing at low temperature is a welldocumented behavior consistent with previous results59,60 and confirmed here for the uncoupled exciton and trion system (see Figure S3). Plasmon narrowing under cooling was also reported previously61 and confirmed here in a control experiment (see Figure S1). The plasmon decay rate at 6 K can be as narrow as 110 meV and up to 150 meV for particles with similar morphology as the ones studied in the hybrid system (see Figure S1). We adopt an average value of γpl = 130 meV for the plasmon line width. The exciton and trion line widths at this temperature can be extracted from the corresponding PL (or reflectivity) spectra, yielding γX = 10 meV and γT = 20 meV, respectively. These values are much narrower than the plasmon resonance width. The collective plasmon−exciton−trion interaction at this temperature thus satisfies a simplified strong coupling criterion as ΩUP−LP > γpl > (γpl + γX,T)/2. Moreover, the emergence of three polariton bands also allows to experimentally measure the splittings between the upper and middle polariton and middle and lower polariton, respectively. These splittings extracted at the zero detuning between plasmon and exciton and plasmon and trion bands respectively are ΩUP−MP ≈ 81 meV and ΩMP−LP ≈ 77 meV and thus both of them individually also satisfy the simplified strong coupling condition as ΩUP−MP, ΩMP−LP > (γpl + γX,T)/2. However, due to the above-mentioned complexity of the eigenvalue problem in this case, these criteria should be considered as crude estimations only. In Numerical Calculations, we complement these estimations with more solid arguments such as observation of anticrossing in absorption spectra of the coupled

The results are shown in Figure 3 with corresponding spectra plotted in Figure S2. Figure 3a depicts the resulting dispersion curves at room temperature. In order to claim strong coupling, one needs to observe anticrossing behavior between the involved resonances. Moreover, the mode splitting needs to be larger than the decay rate of the polaritonic eigenstates. The Rabi splitting is extracted as the minimal splitting between the two polariton branches, which occurs at zero detuning. For T = 300 K, the analysis yields Rabi splitting of Ω ≈ 120 meV. This value has to be compared with the plasmon and exciton line widths. The line widths of the noninteracting plasmonic nanoparticles are measured in an independent experiment and yield γpl ≈ 190 meV (see Figure S1 for details) and the exciton width γX = 20 meV. One thus finds that Ω > (γpl + γX)/2, implying that the system satisfies the strong coupling criterion.2,58 The resulting Hopfield coefficients of the upper and lower polariton versus the plasmon energy are shown in Figure 3a and display a standard plasmon−exciton intermixing behavior, whose contribution depends on the plasmon−exciton detuning. We note that the Rabi splitting observed in this study exceeds those in recently reported observations claiming strong coupling on individual nanoantenna level at room temperature,24,25 likely due to a more compressed mode volume of Ag nanoprisms used in this study. In Numerical Calculations, we further discuss this point and complement the experimental scattering results with calculated absorption spectra and anticrossing. We thus conclude that the mode splitting observed at room temperature arises due to strong coupling between nanoparticle plasmons and neutral excitons in WS2. Let us now turn our attention to the more interesting low temperature case T = 6 K (Figure 3b). In this case, we observe emergence of three anticrossed bands, corresponding to upper, middle, and lower polaritons. We notice immediately (see eq 1b) that at low temperatures the splitting between any polaritonic branches depends on both plasmon−exciton gX and plasmon−trion gT coupling strengths, as well as the resonant frequencies and widths of all contributing parts, resulting in no simple analytical expressions for polariton 1780


Letter

Nano Letters

Figure 4. Numerical calculations. (a,b) Scattering cross sections spectra as a function of temperature. At T = 300 K, the dielectric function of WS2 was assumed to have only one resonance energy corresponding to uncharged exciton X, while at T = 6 K both T and X contribute to the signal. The points as well as the curves are the experimental data and the fitting obtained in Figure 3. Parameters of the model: εAg(ω) dielectric function for silver is taken from Palik,63 WS2 from ref 10 nanoprism side length L = 70 nm, height H = 10 nm, nanoprism edges are rounded with radius of curvature r ∼ 5 nm. TMDC layer was positioned on a dielectric slab with refracting index n = 1.5 that mimics a glass substrate. The whole system is embedded in vacuum. (c) Scattering cross section at zero detuning for 300 and 6 K. (d) Total, silver and WS2 absorption cross sections spectra as a function of temperature. Note splitting observed at both temperatures, which confirms the intermediate coupling regime. (e) Electromagnetic energy density distribution within the nanoparticle and the 2D material at λ = 577. Note logarithmic scale. Both top and side views are shown. Scale bar = 30 nm.

number of particles interacting with the plasmonic field is conserved in the experiments. Numerical Calculations. We have previously shown that observation of anticrossing in scattering data of individual plasmonic nanoparticles cannot alone warrant reaching the strong coupling,64 as such anticrossing can be confused with enhanced absorption65 or Fano resonance regime.66 The safest way to rule out the weak coupling scenario is to increase the Rabi splitting until it significantly overcomes the plasmon line width. This was achieved previously in J-aggregate based systems in scattering6,7 and photoluminescence8 experiments. In the case studied here, the observed splitting does not significantly overcome the plasmon line width. Thus, to draw a definitive conclusion about the regime of interaction in this study, we perform additional numerical calculations, which show that anticrossing is observed not only in scattering, but also in absorption of the coupled system and its constituents. These calculations provide additional evidence that the strong coupling scenario in these experiments is indeed achieved.65 Numerical calculations were performed using the finitedifference time domain (FDTD) method (see Methods). We first perform the numerical anticrossing calculation in a manner similar to our previous study.65 In particular, we fit the dielectric function of Ag by the Drude dispersion model and then vary the plasma frequency. This allows one to tune the plasmon resonance with respect to the exciton at 300 K, whose permittivity is extracted from literature and used without any further open parameters.10 By doing so we obtain the anticrossing curves while only slightly changing the coupling conditions on account of the mode volume being predom-

system. On the basis of these calculations, we conclude that the mode splitting observed at 6 K arises due to just reached strong coupling between nanoparticle plasmons and excitons and trions in WS2. We note that the Hopfield coefficients show that all the polariton branches arise as a result of contribution from all the system components−plasmons, excitons, and trions (see Figure 3b right panel). Thus, in the coupled plasmon−exciton−trion system the intermixing of all three system constituents is observed. This is a very intriguing situation, because it implies that all the polariton branches possess nonzero net electrical charge. For this reason, these hybrid states can potentially have an impact on charge transport, a situation reported recently in an organic semiconductor microcavity system.48 Optical nonlinearity should also be strongly affected by the Fermionic nature of the trion which can result in strong nonlinear behavior compared to the pure bosonic case of a neutral exciton. The plasmon−exciton (and plasmon−trion) coupling rates can be deduced by fitting the experimental anticrossing data in Figure 3. The extracted values from the fitting give gX ≈ 74 meV for room temperature, and gX ≈ 54 meV and gT ≈ 59 meV for 6 K. The emergence of gT, together with the reduction of gX, can be attributed to a redistribution of oscillator strength from excitons to trions upon cooling. This is consistent with both PL and reflectivity data measured on bare WS2 monolayers (see Figure S3) and can be explained by the amount of p-doping in the WS2 and the increased stability of the trion at low temperature.62 Another important observation is that g2X(T = 300 K) ≈ g2X(T = 6 K) + g2T(T = 6 K), indicating that a total 1781


Letter

Nano Letters

coupled plasmon−exciton−trion polariton system comprising a silver nanoprism and monolayer WS2 is very useful for practical realization of strong coupling. Discussion. To conclude, we have demonstrated that the optical response of the strongly coupled system can be tailored by tuning the temperature. At low temperatures, the plasmonic cavity strongly interacts with excitons and trions in the monolayer WS2, whereas at room temperature only the neutral exciton is coupled to the plasmon. We note that the temperature-dependent PL signal of the WS2 monolayer and in particular the second resonance at low energy appearing upon decreasing of temperature follows the trend associated with the trion state.13 Other low energy states like bound states or localized excitons50,51 have lower dissociation energies and are not stable at elevated temperatures.72 Moreover, the bound states have low oscillator strength.56 On the basis of this, we assign the low energy peak observed in the PL spectrum (Figure 1b) and the low energy dip in the scattering spectra (Figure 2) to the trion. Here, the trion state is stabilized by low temperature and chemical p-doping.54 We note that there are several other processes that may play an important role in our study and in general in plasmonTMDC coupled systems. First, a charge transfer process between monolayer TMDC and metallic surfaces can occur as a result of the proximity effect.73 This can potentially affect the behavior of the coupled system; however, in this study the 2D material and Ag nanoprism were separated by a polymer and citrate stabilizing layers, which prevent direct metal−TMDC contact. Second, exciton and trion states in close proximity to a metallic surface may have renormalized binding energies and oscillator strength due to nonlocal screening effects, which is unique for 2D materials.74 This effect can also affect the behavior of the coupled system; however, in our DF scattering data we do not observe large renormalization effects. Finally, the plasmon−trion coupling here, gT ≈ 70 meV, exceeds the trion binding energy, ωX − ωT ≈ 40 meV, which is an interesting regime because the light-matter coupling surpasses the Coulomb interaction in this case. These effects may have an impact on plasmon−exciton−trion interactions in the present case and were not taken into account in the FDTD calculations. Future theoretical investigations involving the quantum mechanical nature of interacting quasiparticles are needed to properly account for these interactions. In this work, we achieve strong coupling with the Rabi splitting of ∼120 meV at room temperature, which is higher than in previous realizations.24,25 In addition to that we also demonstrate formation of plasmon−exciton−trion polaritons at low temperature. Trions were observed previously in more extended systems, like microcavities and plasmonic lattices.42−44,46 However, in the present case this is achieved at a truly nanoscopic scale of an individual nanoparticle and with a very small number of involved trions and excitons, making this contribution especially interesting for quantum and nonlinear applications.75,76 On the basis of the analysis above, it is tempting to estimate the number of excitons contributing to the coupling process in this case, especially keeping in mind the large transition dipole moment of WS2. Our estimation is based on the well-known relation for the coupling strength g = N μe |Evac|=

inantly defined by the geometrical volume of the particle. This is shown in Figure 4a (plasmon−exciton coupling). We then superimpose the numerical anticrossing in scattering with the experimental data from Figure 3a and find a striking agreement between experimental and theoretical results (see Figure 4a). We thus proceed to resolve anticrossing in total absorption as well as in its individual components, Ag nanoprism and the WS2 monolayer, which all exhibit the anticrossing behavior, thereby proving that strong coupling is reached in this system65 (see Figure 4a). Additionally, in Figure 4c we plot the scattering spectrum obtained for the case of zero detuning. Excellent matching to experimental spectra is observed, considering the only free parameter is the size of the Ag nanoprism. Of course, this freedom is limited by the span of dimensions of the Ag nanoprism observed in SEM. To conduct a corresponding study of the plasmon−exciton− trion system, we first model it at zero detuning to match the exciton and trion lines to experimental data (see Methods) with the nanoprism size fixed in the previous calculations. The matching of the numerical scattering spectrum (Figure 4c) and the experimental one (Figure 2) demonstrates the correctness of our phenomenological description of the exciton and trion at 6 K. We thus proceed to investigate anticrossing, with results shown in Figure 4b The computed scattering spectra for the plasmon−exciton− trion case match extremely well with the experimental anticrossing (overlaid points) as shown in Figure 4b. The total absorption as well as its components in Ag nanoprism and the WS2 monolayer also exhibit the anticrossing behavior between the three hybrid eigen states (see Figure 4b). With our Ag−WS2 model validated, we plot the absorption cross-section of the coupled system along with its components in Figure 4d. The data show clear splitting of absorption in the Ag nanoprism, on the other hand, the absorption spectra of the WS2 monolayers shows only a shoulder development, demonstrating that our system is marginally reaching the strong coupling regime.65 The small splitting in the 2D material absorption is explained by a lack of long-lived oscillations between Ag and WS2. As shown in Figure S6, the time evolution of the Rabi oscillations is short-lived and exhibits only one significant period. A similar observation can be drawn from the oscillations of the electric fields around the Ag triangle, where the excitation energy alternates between the plasmon− polariton (visible enhanced fields) and the 2D material (see SI Movie 1 and Movie 2). We further inspect the electromagnetic energy density distributions67 in the coupled system (Figure 4e). We observe that the mode in the nanoprism is confined mainly to its interior. We also observe that while the energy density in the WS2 is greater than in Ag, the monolayer occupies only a small volume due to its two-dimensionality and therefore the total energy stored in the metal and the 2D material is similar. For single nanoparticles the mode is concentrated within its volume68−70 and to obtain long-lived Rabi oscillations the excitonic material needs not only a large transition dipole moment, but it is also necessary to maximize the overlap between the plasmonic field mode and the exciton states,7,66 what in the present case would ideally amount to saturating the small fraction of the mode volume located outside the metal resonator. Here this is not possible (Figure 4e), yet filling up a small fraction of the mode volume with the 2D material is enough to reach strong coupling, due to the large transition dipole moment of WS2 (μe ≈ 56 D71). We thus conclude that a

N μe ℏω/(2εε0V ) . For the nanotriangles considered in the present work (side lengths in the range 60−80 and 10 nm 1782


Letter

Nano Letters thick), the geometrical volume is on the order of (1.5−2.8) × 104 nm3. For such small single particles the mode volume is mainly determined by the geometrical one, however, a nearby high-refractive index material can substantially decrease it.66 In our case, the high background permittivity of monolayer WS2 decreases the mode volume by approximately 50%. Thus, using the above quoted lower bound of V = 0.7 × 104 nm3, a value which was verified in FDTD calculations using the approach for dispersive weakly radiating cavities,68 and μe = 56 D for an exciton resonant at 2 eV coupled to such a cavity yields a coupling strength of ∼30 meV. To account for the measured splitting of 120 meV at room temperature the required coupling strength needs to be gX ≈ 74 meV due to the mismatch in the plasmon and exciton widths. Hence, the upper bound of the number of excitons is NX < 10. The measured Rabi splitting at 6 K is around 150 meV, giving an approximate exciton and trion coupling strength of gX ≈ gT ≈ 50 meV. As the energy difference of both transitions is negligible for the purposes of this estimation, in both cases the expected lower bound on the number of interacting excitons and trions is NX ≈ NT < 5, when accounting for the influence of the permittivity of the surrounding material. This number closely approaches the quantum optics limit of N = 1, thus making this system potentially interesting for studying photon−photon interactions at the nanoscale. Moreover, due to Coulomb repulsion charged exciton-polaritons are expected to interact with each other stronger than their neutral counterparts. Thus, this system might exhibit stronger nonlinear response as compared to a purely bosonic situation. More generally, our findings demonstrate the principal possibility of studying electrically charged polaritons in a form of plasmon−exciton−trion hybrids. Here, this is done at low temperature to ensure the trion stability, however, by stabilization of the trion state by other means, for example, by electrostatic doping, similar effects can be anticipated at room temperature.46,47,49 Constructing macroscopic coherent polariton states that will constitute a coherent mixture of excitons, trions, and cavity excitations may find use in charge transport and optoelectronic devices by boosting the carrier mobility48 in analogous way to the theoretically predicted exciton transport enhancement mediated by a cavity.77,78 This new degree of freedom, charged polaritons, is the central observation of this work. In view of the discussion above, we envision that these findings may find potential implications for various optoelectronic applications, such as light harvesting and light-emitting devices, and for strong photon−photon interactions. Methods. Sample Preparation. Silver nanoprisms were synthesized from solution using a seed-mediated protocol. WS2 were mechanically exfoliated from bulk crystal (HQ-graphene) and transferred to a Si wafer with a thermally oxide layer (50 nm-thick) using the all-dry transfer method.79 Monolayers were identified by photoluminescence spectra and optical contrast. In order to ensure a proper density of nanoprisms covering the monolayer flake, an adhesion layer (Polylysine 0.25 mg/mL) was deposited before applying the nanoprism solution. The nanoparticle solution was drop-casted and allowed to rest at the sample surface for 2 min. The excess of solution is gently removed by an absorptive tissue. We note that the polymer layer that we utilize to adhere silver nanoprisms to the monolayer WS2 plays an important role in the stabilization of the trions. This is likely induced by the chemical doping.54 The trion in this case is mostly a

positively charged state because the adhesion layer tends to pdope WS2. To demonstrate this, in the Supporting Information (see Figure S4) we perform a control experiment which shows that strong plasmon−trion coupling is not observed in the absence of the polylysine adhesion layer even at cryogenic temperatures. Optical Measurements. Dark-field optical microscopy and spectroscopy measurements were done using a laser driven light source (ENERGETIQ EQ-99XFC) with side illumination configuration at an angle of about 50°. For photoluminescence experiments, the sample was excited by a CW 532 nm (2.33 eV) laser under irradiance of ∼100 W/cm2. PL and DF signals were collected using a 20× objective (Nikon, NA = 0.45) and directed to a fiber-coupled 30 cm spectrometer (Andor Shamrock SR-303i) equipped with a CCD detector (Andor iDus 420). Low-temperature measurements were performed using a coldfinger optical cryostat (Janis). FDTD Anticrossing. FDTD calculations were carried out using the commercial solver from Lumerical, Inc. The silver prisms are assumed to be triangular in shape with an edge length in the range of 60−80 nm, thickness 10 nm, edge rounding of 3 nm and corner rounding of 10 nm. They are modeled as a dispersive Drude metal with parameters obtained by fitting tabulated data from Palik with ϵ∞ = 3.7, ωp = 13 PHz, and γ = 180 THz to match the experimental permittivity around 600 nm. For anticrossing studies the plasma frequency was varied from about 7 to 10 eV. The silver prisms in experiments are coated by a molecular stabilizing layer which was modeled as a dispersionless dielectric with a refractive index of 1.4. The dielectric susceptibility of WS2 monolayer at room temperature (corresponding solely due to neutral exciton contribution) is taken from literature and is used without further modification.10 To obtain the permittivity of a WS2 monolayer at 6 K we use reflectivity and photoluminescence measurements (see Figure S3) to estimate the exciton and trion line widths and spectral positions. The oscillator strengths of a 1 nm thick layer representing the WS2 monolayer are based on available literature and further refined based on our own measurements in FDTD by matching the calculated and experimental scattering spectra. The monolayer and coated Ag nanoprism are placed on a glass substrate (n = 1.45) and illuminated by a plane wave at normal incidence. The meshing which assured converged results was 0.5 nm in the x- and ydirections (transverse) and 0.2 nm in the longitudinal direction (z-axis).

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.7b04965. Bare nanoprism spectra versus temperature; dark-field scattering anti-crossing data; reflectivity and photoluminescence of monolayer WS2 versus temperature and versus adhesion layer; coupled system without adhesion layer; semiconductor PL versus temperature fit by O’Donnel model; visualisation of Rabi oscillations; additional references (PDF) Excitation energy alternating between the plasmon− polariton (visible enhanced fields) and the 2D material (MPG) 1783


Letter

Nano Letters

■

(18) Sun, Z.; Gu, J.; Ghazaryan, A.; Shotan, Z.; Considine, C. R.; Dollar, M.; Chakraborty, B.; Liu, X.; Ghaemi, P.; Kéna-Cohen, S.; Menon, V. M. Nat. Photonics 2017, 11 (8), 491−496. (19) Liu, X.; Galfsky, T.; Sun, Z.; Xia, F.; Lin, E.-c.; Lee, Y.-H.; KénaCohen, S.; Menon, V. M. Nat. Photonics 2015, 9 (1), 30−34. (20) Dufferwiel, S.; Schwarz, S.; Withers, F.; Trichet, A. A. P.; Li, F.; Sich, M.; Del Pozo-Zamudio, O.; Clark, C.; Nalitov, A.; Solnyshkov, D. D.; Malpuech, G.; Novoselov, K. S.; Smith, J. M.; Skolnick, M. S.; Krizhanovskii, D. N.; Tartakovskii, A. I. Nat. Commun. 2015, 6, 8579. (21) Sidler, M.; Back, P.; Cotlet, O.; Srivastava, A.; Fink, T.; Kroner, M.; Demler, E.; Imamoglu, A. Nat. Phys. 2016, 13 (3), 255−261. (22) Liu, W.; Lee, B.; Naylor, C. H.; Ee, H.-S.; Park, J.; Johnson, A. T. C.; Agarwal, R. Nano Lett. 2016, 16 (2), 1262−1269. (23) Wang, S.; Li, S.; Chervy, T.; Shalabney, A.; Azzini, S.; Orgiu, E.; Hutchison, J. A.; Genet, C.; Samorì, P.; Ebbesen, T. W. Nano Lett. 2016, 16 (7), 4368−4374. (24) 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 Lett. 2017, 17 (8), 4689−4697. (25) Zheng, D.; Zhang, S.; Deng, Q.; Kang, M.; Nordlander, P.; Xu, H. Nano Lett. 2017, 17 (6), 3809−3814. (26) Kern, J.; Trügler, A.; Niehues, I.; Ewering, J.; Schmidt, R.; Schneider, R.; Najmaei, S.; George, A.; Zhang, J.; Lou, J.; Hohenester, U.; Michaelis de Vasconcellos, S.; Bratschitsch, R. ACS Photonics 2015, 2 (9), 1260−1265. (27) Najmaei, S.; Mlayah, A.; Arbouet, A.; Girard, C.; Léotin, J.; Lou, J. ACS Nano 2014, 8 (12), 12682−12689. (28) Butun, S.; Tongay, S.; Aydin, K. Nano Lett. 2015, 15 (4), 2700− 2704. (29) Lee, B.; Park, J.; Han, G. H.; Ee, H.-S.; Naylor, C. H.; Liu, W.; Johnson, A. T. C.; Agarwal, R. Nano Lett. 2015, 15 (5), 3646−3653. (30) Chen, H.; Yang, J.; Rusak, E.; Straubel, J.; Guo, R.; Myint, Y. W.; Pei, J.; Decker, M.; Staude, I.; Rockstuhl, C.; Lu, Y.; Kivshar, Y. S.; Neshev, D. Sci. Rep. 2016, 6, 22296. (31) Li, J.; Ji, Q.; Chu, S.; Zhang, Y.; Li, Y.; Gong, Q.; Liu, K.; Shi, K. Sci. Rep. 2016, 6, 23626. (32) Moilanen, A. J.; Hakala, T. K.; Törmä, P. ACS Photonics 2018, 5 (1), 54. (33) Schwartz, T.; Hutchison, J. A.; Genet, C.; Ebbesen, T. W. Phys. Rev. Lett. 2011, 106 (19), 196405. (34) Baudrion, A.-L.; Perron, A.; Veltri, A.; Bouhelier, A.; Adam, P.M.; Bachelot, R. Nano Lett. 2013, 13 (1), 282−286. (35) Vasa, P.; Pomraenke, R.; Cirmi, G.; De Re, E.; Wang, W.; Schwieger, S.; Leipold, D.; Runge, E.; Cerullo, G.; Lienau, C. ACS Nano 2010, 4 (12), 7559−7565. (36) Vasa, P.; Wang, W.; Pomraenke, R.; Lammers, M.; Maiuri, M.; Manzoni, C.; Cerullo, G.; Lienau, C. Nat. Photonics 2013, 7 (2), 128− 132. (37) Abid, I.; Chen, W.; Yuan, J.; Bohloul, A.; Najmaei, S.; Avendano, C.; Péchou, R.; Mlayah, A.; Lou, J. ACS Photonics 2017, 4 (7), 1653− 1660. (38) Liu, X.; Bao, W.; Li, Q.; Ropp, C.; Wang, Y.; Zhang, X. Phys. Rev. Lett. 2017, 119 (2), 027403. (39) Rodriguez, S. R. K.; Feist, J.; Verschuuren, M. A.; Garcia Vidal, F. J.; Gómez Rivas, J. Phys. Rev. Lett. 2013, 111 (16), 166802. (40) Väkeväinen, A. I.; Moerland, R. J.; Rekola, H. T.; Eskelinen, A. P.; Martikainen, J. P.; Kim, D. H.; Törmä, P. Nano Lett. 2014, 14 (4), 1721−1727. (41) Ramezani, M.; Halpin, A.; Fernández-Domínguez, A. I.; Feist, J.; Rodriguez, S. R.-K.; Garcia-Vidal, F. J.; Gómez Rivas, J. Optica 2017, 4 (1), 31−37. (42) Rapaport, R.; Harel, R.; Cohen, E.; Ron, A.; Linder, E.; Pfeiffer, L. N. Phys. Rev. Lett. 2000, 84 (7), 1607−1610. (43) Rapaport, R.; Qarry, A.; Cohen, E.; Ron, A.; Pfeiffer, L. N. Phys. Status Solidi B 2001, 227 (2), 419−427. (44) Rapaport, R.; Cohen, E.; Ron, A.; Linder, E.; Pfeiffer, L. N. Phys. Rev. B: Condens. Matter Mater. Phys. 2001, 63 (23), 235310. (45) Rakher, M. T.; Stoltz, N. G.; Coldren, L. A.; Petroff, P. M.; Bouwmeester, D. Phys. Rev. Lett. 2009, 102 (9), 097403.

Excitation energy alternating between the plasmon− polariton (visible enhanced fields) and the 2D material (MPG)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Tomasz J. Antosiewicz: 0000-0003-2535-4174 Timur Shegai: 0000-0002-4266-3721 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We acknowledge financial support from Knut and Alice Wallenberg Foundation and Engkvist Foundation. T.J.A. thanks the Polish Ministry of Science and Higher Education for support via the Iuventus Plus Project IP2014 000473 as well as the Swedish Foundation for Strategic Research via the project SSF RMA 11. T.S. acknowledges financial support from the Swedish Research Council (Vetenskapsområdet, Grant No. 2016-06059).

■

REFERENCES

(1) Raimond, J. M.; Brune, M.; Haroche, S. Rev. Mod. Phys. 2001, 73 (3), 565−582. (2) Khitrova, G.; Gibbs, H. M.; Kira, M.; Koch, S. W.; Scherer, A. Nat. Phys. 2006, 2 (2), 81−90. (3) Smolka, S.; Wuester, W.; Haupt, F.; Faelt, S.; Wegscheider, W.; Imamoglu, A. Science 2014, 346 (6207), 332−335. (4) Törmä, P.; Barnes, W. L. Rep. Prog. Phys. 2015, 78 (1), 013901. (5) Baranov, D. G.; Wersäll, M.; Cuadra, J.; Antosiewicz, T. J.; Shegai, T. ACS Photonics 2018, 5, 24. (6) Schlather, A. E.; Large, N.; Urban, A. S.; Nordlander, P.; Halas, N. J. Nano Lett. 2013, 13 (7), 3281−3286. (7) Zengin, G.; Wersäll, M.; Nilsson, S.; Antosiewicz, T. J.; Käll, M.; Shegai, T. Phys. Rev. Lett. 2015, 114 (15), 157401. (8) Wersäll, M.; Cuadra, J.; Antosiewicz, T. J.; Balci, S.; Shegai, T. Nano Lett. 2017, 17 (1), 551−558. (9) Mak, K. F.; Lee, C.; Hone, J.; Shan, J.; Heinz, T. F. Phys. Rev. Lett. 2010, 105 (13), 136805. (10) 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. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 90 (20), 205422. (11) Amani, M.; Taheri, P.; Addou, R.; Ahn, G. H.; Kiriya, D.; Lien, D.-H.; Ager, J. W.; Wallace, R. M.; Javey, A. Nano Lett. 2016, 16 (4), 2786−2791. (12) Mak, K. F.; He, K.; Lee, C.; Lee, G. H.; Hone, J.; Heinz, T. F.; Shan, J. Nat. Mater. 2013, 12 (3), 207−211. (13) Ross, J. S.; Wu, S.; Yu, H.; Ghimire, N. J.; Jones, A. M.; Aivazian, G.; Yan, J.; Mandrus, D. G.; Xiao, D.; Yao, W.; Xu, X. Nat. Commun. 2013, 4, 1474. (14) Ross, J. S.; Klement, P.; Jones, A. M.; Ghimire, N. J.; Yan, J.; Mandrus, D. G.; Taniguchi, T.; Watanabe, K.; Kitamura, K.; Yao, W.; Cobden, D. H.; Xu, X. Nat. Nanotechnol. 2014, 9 (4), 268−272. (15) Mak, K. F.; He, K.; Shan, J.; Heinz, T. F. Nat. Nanotechnol. 2012, 7 (8), 494−498. (16) Zeng, H.; Dai, J.; Yao, W.; Xiao, D.; Cui, X. Nat. Nanotechnol. 2012, 7 (8), 490−493. (17) Dufferwiel, S.; Lyons, T. P.; Solnyshkov, D. D.; Trichet, A. A. P.; Withers, F.; Malpuech, G.; Smith, J. M.; Novoselov, K. S.; Skolnick, M. S.; Krizhanovskii, D. N.; Tartakovskii, A. I.; et al. Nat. Photonics 2017, 11 (8), 497−501. 1784


Letter

Nano Letters

(79) Castellanos-Gomez, A.; et al. 2D Mater. 2014, 1 (1), 011002.

(46) Lee, B.; Liu, W.; Naylor, C. H.; Park, J.; Malek, S. C.; Berger, J. S.; Johnson, A. T. C.; Agarwal, R. Nano Lett. 2017, 17 (7), 4541−4547. (47) Li, B.; Zu, S.; Zhou, J.; Jiang, Q.; Du, B.; Shan, H.; Luo, Y.; Liu, Z.; Zhu, X.; Fang, Z. ACS Nano 2017, 11 (10), 9720−9727. (48) Orgiu, E.; George, J.; Hutchison, J. A.; Devaux, E.; Dayen, J. F.; Doudin, B.; Stellacci, F.; Genet, C.; Schachenmayer, J.; Genes, C.; Pupillo, G.; Samori, P.; Ebbesen, T. W. Nat. Mater. 2015, 14 (11), 1123−1129. (49) Zhu, B.; Chen, X.; Cui, X. Sci. Rep. 2015, 5, 9218. (50) Jones, A. M.; Yu, H.; Ghimire, N. J.; Wu, S.; Aivazian, G.; Ross, J. S.; Zhao, B.; Yan, J.; Mandrus, D. G.; Xiao, D.; Yao, W.; Xu, X. Nat. Nanotechnol. 2013, 8 (9), 634−638. (51) Wang, G.; Bouet, L.; Lagarde, D.; Vidal, M.; Balocchi, A.; Amand, T.; Marie, X.; Urbaszek, B. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 90 (7), 075413. (52) Liu, B.; Zhao, W.; Ding, Z.; Verzhbitskiy, I.; Li, L.; Lu, J.; Chen, J.; Eda, G.; Loh, K. P. Adv. Mater. 2016, 28 (30), 6457−6464. (53) Xu, W.; Liu, W.; Schmidt, J. F.; Zhao, W.; Lu, X.; Raab, T.; Diederichs, C.; Gao, W.; Seletskiy, D. V.; Xiong, Q. Nature 2017, 541 (7635), 62−67. (54) Mouri, S.; Miyauchi, Y.; Matsuda, K. Nano Lett. 2013, 13 (12), 5944−5948. (55) Jin, R.; Cao, C. Y.; Hao, E.; Metraux, G. S.; Schatz, G. C.; Mirkin, C. A. Nature 2003, 425, 487−490. (56) Kavokin, A. V. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50 (11), 8000−8003. (57) Hopfield, J. J. Phys. Rev. 1958, 112 (5), 1555−1567. (58) Savasta, S.; Saija, R.; Ridolfo, A.; Di Stefano, O.; Denti, P.; Borghese, F. ACS Nano 2010, 4 (11), 6369−6376. (59) 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. Nat. Commun. 2015, 6, 8315. (60) Dey, P.; Paul, J.; Wang, Z.; Stevens, C. E.; Liu, C.; Romero, A. H.; Shan, J.; Hilton, D. J.; Karaiskaj, D. Phys. Rev. Lett. 2016, 116 (12), 127402. (61) Liu, M.; Pelton, M.; Guyot-Sionnest, P. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 79 (3), 035418. (62) Arora, A.; Koperski, M.; Nogajewski, K.; Marcus, J.; Faugeras, C.; Potemski, M. Nanoscale 2015, 7 (23), 10421−10429. (63) Palik, E. D. Handbook of Optical Constants of Solids I; Academic Press: San Diego, 1998. (64) Zengin, G.; Johansson, G.; Johansson, P.; Antosiewicz, T. J.; Käll, M.; Shegai, T. Sci. Rep. 2013, 3, 3074. (65) Antosiewicz, T. J.; Apell, S. P.; Shegai, T. ACS Photonics 2014, 1 (5), 454−463. (66) Yang, Z.-J.; Antosiewicz, T. J.; Shegai, T. Opt. Express 2016, 24 (18), 20373−20381. (67) Ruppin, R. Phys. Lett. A 2002, 299 (2−3), 309−312. (68) Koenderink, A. F. Opt. Lett. 2010, 35 (24), 4208−4210. (69) Sauvan, C.; Hugonin, J. P.; Maksymov, I. S.; Lalanne, P. Phys. Rev. Lett. 2013, 110 (23), 237401. (70) Kristensen, P. T.; Hughes, S. ACS Photonics 2014, 1 (1), 2−10. (71) Sie, E. J.; McIver, J. W.; Lee, Y.-H.; Fu, L.; Kong, J.; Gedik, N. Nat. Mater. 2015, 14 (3), 290−294. (72) Ganchev, B.; Drummond, N.; Aleiner, I.; Fal’ko, V. Phys. Rev. Lett. 2015, 114 (10), 107401. (73) Chhowalla, M.; Jena, D.; Zhang, H. Nat. Rev. Mater. 2016, 1, 16052. (74) Qiu, D. Y.; da Jornada, F. H.; Louie, S. G. Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 93 (23), 235435. (75) Santhosh, K.; Bitton, O.; Chuntonov, L.; Haran, G. Nat. Commun. 2016, 7, ncomms11823. (76) 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. (77) Feist, J.; Garcia-Vidal, F. J. Phys. Rev. Lett. 2015, 114 (19), 196402. (78) Schachenmayer, J.; Genes, C.; Tignone, E.; Pupillo, G. Phys. Rev. Lett. 2015, 114 (19), 196403. 1785


Observation of tunable charged exciton polaritons ... - ACS Publications

Recommend Documents