Simultaneous control of plasmon–exciton and plasmon–trion couplings in an Au nanosphere and monolayer WS₂ hybrid system

Two-dimensional transition metal dichalcogenides (TMDs) are promising building blocks for future optoelectronic and photonic devices owing to their striking optical properties and highly flexible features for integration.¹ In contrast to their bulk counterparts, monolayer TMDs have a direct bandgap and a large transition dipole that allows a strong coupling with light.^2,3 Due to the strong geometrical confinement and weak dielectric screening, monolayer TMDs show strong Coulomb interactions, making the bound electron–hole pair (exciton) even survive at room temperature.^4,5 Additionally, the large exciton binding energy allows us to readily observe the higher-order excitonic quasiparticles, for example, the trion.^6,7 The rich variety of excitonic effects make the TMDs an intriguing platform to implement room-temperature excitonic devices, including light-emitting diodes (LEDs),⁸ photodetectors,^9,10 and nanolasers.¹¹ In particular, integrating monolayer TMDs with nanophotonic structures (e.g., photonic crystal cavity) can eliminate the obstacles of the intrinsic weak absorption and low quantum yield inherited from the monolayer nature, promoting the performance of monolayer TMDs based devices.¹² 

Plasmonic structures, relying on the virtue of strong local field enhancement, provide alternative solutions to boost light–matter interactions at the nanoscale.^13,14 As the fundamental element, metallic nanoparticles, acting as a nanocavity or nanoantenna, are widely used to explore the plasmon–exciton couplings in monolayer TMDs.¹⁵ Generally, the coupling strength is determined by the inner product between the transition dipole moment of the exciton and the dipolar electric field of the plasmon.¹⁶ When the hybrid system of a metal nanoparticle and a monolayer TMD falls into the weak coupling region, the spontaneous emission rate of the exciton can be accelerated via the Purcell effect, leading to the enhancement of photoluminescence (PL).^1,17,18 On the other hand, if the coupling strength is sufficiently strong, the energy exchange rate between the exciton and plasmon will be larger than the respective decoherence rates, resulting in a hybrid light–matter state (plexciton) featured with an energy difference, i.e., Rabi splitting.^16,19 Furthermore, the plasmonic responses of metallic nanoparticles, such as the resonance frequency and the local field distribution, can be well controlled by modifying the size,^20,21 shape,²² and surrounding medium of nanoparticles.²³ These features make it flexible to spectrally and spatially tailor the overlap between the plasmon near-field and the exciton in monolayer TMDs, permitting a comprehensive scan of different coupling states of the hybrid system.

As a typical TMD, the monolayer WS₂ supports both the exciton and trion that play a pronounced role in its optical properties.²⁴ The monolayer WS₂ has been integrated with a variety of plasmonic structures, such as single metallic nanoparticles,^25–28 antenna arrays,^29–32 particle-on-mirror nanocavities,^33–35 and tip–substrate nanocavities,³⁶ providing an effective tool for controlling the coupling between the plasmon and excitonic quasiparticles. Moreover, due to the existence of the trion, such light–matter coupling in the hybrid system can be readily manipulated by electrical gating,^8,37,38 chemical doping,³⁹ and dielectric screening.^40,41 These methods usually rely on the sophisticated designs and/or the cryogenic temperatures. For practical applications, it is highly desirable to control the plasmon–excitonic quasiparticle coupling with a facile hybrid system operating in ambient conditions, which, however, has not been fully explored yet.

To this end, we propose a method to control the coupling between the surface plasmon and the exciton, as well as the trion, in a hybrid system composed of a monolayer WS₂ and an Au nanosphere. Owing to the strong dispersion of the surface plasmon against the particle size, the hybrid system is readily tuned from the dominated plasmon–exciton coupling to the plasmon–exciton–trion coupling by simply changing the radius of the Au nanosphere. Interestingly, with an appropriate particle size, Fano lineshapes, as a feature of the moderate coupling, are found in the spectral regions of the exciton and the trion. The moderate coupling empowers the hybrid system a remarkable light-emitting capacity that yields PL enhancement factors of 1265- and 680-folds for the exciton and trion emissions, respectively.

Figure 1(a) displays a representative dark-field scattering spectrum of a single Au nanosphere positioned on the SiO₂/Si substrate. This Au nanosphere (Nanoseedz, Inc.) has a radius of r = 70 nm and is capped with a 2 nm-thick cetyltrimethylammonium bromide (CTAB) surfactant polymer. It is found from the spectrum that the s-polarized beam produces a strong plasmon resonance centered at 560 nm with the peak width of 322 meV derived from the Lorentzian fitting. We simulate the charge distribution and electric field enhancement map of the Au nanosphere (r = 70 nm) on the SiO₂/Si substrate using the finite-difference time-domain (FDTD) method. According to the charge distribution shown in Fig. 1(b), this spectral peak is attributed to an electric dipole mode. Figure 1(c) displays the electric field enhancement map of this mode with the enhancement factor as large as 6. As seen, the electric field is mainly localized as two lobes near the nanosphere and a considerable field is concentrated in the gap between the nanosphere and the substrate, which is highly favorable to inserting the monolayer WS₂ to achieve a strong light–matter interaction.

Figure 2(a) schematically shows the hybrid system composed of an Au nanosphere sitting on an exfoliated monolayer WS₂ flake, which is encapsulated by a 2 nm-thick Al₂O₃ spacer to avoid the PL quenching. In Fig. 2(b), we display the dark-field and scanning electronic microscopy (SEM) images of the hybrid system. The monolayer nature of the WS₂ flake is confirmed by the Raman spectrum using a commercial confocal microscope (WITec, Alpha 300R). Figure 2(c) shows six observable Raman modes, including A_1g(M)-LA(M) (∼232.4 cm⁻¹), 2LA(M)-$2E2g2$(M) (∼296.9 cm⁻¹), 2LA(M)-$E2g2$(Γ) (∼324.2 cm⁻¹), 2LA(M) (∼349.9 cm⁻¹), $E2g1$(Γ) (∼357.3 cm⁻¹), and A_1g(Γ) (∼417.3 cm⁻¹). It is found that in-plane [$E2g1$(Γ)] and out-of-plane phonon modes [A_1g(Γ)] have an interval of 60 cm⁻¹, in coincidence with that of monolayer WS₂ reported in the literature.⁴² The red curve of Fig. 2(d) shows the PL spectrum of a pristine monolayer WS₂, which is contributed from emissions of a higher energy (λ_X = 615 nm) neutral exciton and a lower energy (λ_T = 630 nm) charged exciton (trion). It is found that the trion emission (∼1216 counts) is stronger than that of the exciton (∼844 counts) owing to the electron doping induced by a relative high excitation power (0.6 mW).⁴³ Additionally, compared with the single broad peak of the bare Au nanosphere (r = 100 nm) shown in Fig. S1 of the supplementary material, the scattering spectrum of the hybrid system [blue dots in Fig. 2(d)] exhibits obvious dips around the spectral locations of the exciton and trion of monolayer WS₂, which implies that considerable couplings occur due to the plasmon–exciton and plasmon–trion interactions. Meanwhile, the scattering spectrum of the hybrid system displays a plasmon resonance centered at 518 nm, which is attributed to an electric quadrupole mode [see the charge distribution in Fig. S2(b)].

The plasmon resonance wavelength is strongly dependent on the particle size; therefore, it allows us to examine the hybrid system with different plasmon–exciton (plasmon–trion) detunings by changing the radius of the Au nanosphere. In this sense, Au nanospheres with the radius from 55 to 130 nm are chosen [see the SEM images in Fig. 3(b)], which permits the plasmon resonance wavelength across the resonances of the exciton and the trion as shown in Fig. S1 of the supplementary material. Indeed, the absorption spectrum can provide direct evidence to identify the peak value and the mode splitting to interpret the underlying physics of the resonance coupling between the plasmonic structure and the emitter.³⁰ In fact, the scattering spectrum also reflects the same resonance nature of the system, for example, the resonance wavelength, as the absorption. Specifically, the scattering becomes overwhelming over the absorption when the Au nanoparticle is with a radius over 50 nm.⁴⁴ Therefore, scattering spectroscopy is used as an indispensable tool to probe the plasmon–exciton and plasmon–trion interactions in the single-nanoparticle-level system.^34,45,46 Figure 3(a) shows the normalized scattering spectrum of the hybrid system as a dependence of the nanosphere radius. The scattering spectrum consistently has a dip near the position of the exciton (λ_X = 623 nm), while it exhibits another dip around the location of the trion (λ_T = 633 nm) when the nanosphere radius is over 90 nm.

To provide more insight, we employ the coupled-oscillator model to interpret the coupling state. As illustrated in Fig. 3(c), the plasmon mode, exciton, and trion are represented by oscillators with the resonance frequencies of ω_pl, ω_X, and ω_T and the dissipation rates of γ_pl, γ_X, and γ_T. We assume that there is no direct inter-exciton coupling between the exciton and the trion. Then, the coupling strengths for plasmon–exciton and plasmon–trion interactions are denoted as the spring constants of g_X and g_T. Accordingly, the Hamiltonian of the three-coupled-oscillator model can be written as^30,34

The diagonalization of these Hamiltonians yields the eigenfrequencies and eigenvector components (Hopfield coefficients) of the hybrid system. According to the coupled oscillator model, the scattering spectrum of the hybrid system can be stated as^37,47

where μ_pl denotes the coordinate of the plasmon oscillation and is governed by

Here, F_pl represents the normalized forces driving the motion of the coordinate due to the external electromagnetic field. We then use Eq. (3) to fit the scattering spectrum in Fig. 3(a). The fitting results (solid lines) are in good accordance with the experimental one (dots).

Figure 3(d) summarizes the mode dispersions of the hybrid system against the frequency of plasmon dipole mode (nanosphere radius). Here, the dots are obtained from the scattering spectra in Fig. 3(a), and the solid lines are extracted using the three-coupled-oscillator model with the fitting parameters listed in Table S1 of the supplementary material. As seen, the minimal interval between the upper and lower energy branches (ΔE_up−lp = 89 meV) occurs at the zero detuning between the plasmon dipole mode and exciton, which locates in the red background region of Fig. 3(d) (r < 90 nm). We also note that the peak width of uncoupled plasmon mode varies with the nanosphere size and has an average of γ_pl = 322 meV. According to the Gaussian decomposition of the PL spectrum in Fig. 2(d), the peak widths of the exciton and trion are determined to be γ_X = 32.8 meV and γ_T = 78.9 meV, respectively. Since the energy splitting ΔE_up−lp is larger than excitonic linewidths γ_X,T but smaller than the strong coupling criteria (γ_pl + γ_X,T)/2, the hybrid system enters a moderate coupling regime. To be more rigorous, the minimal splitting between the middle and lower energy branches is determined to be ΔE_md−lp = 48 meV at the zero detuning between the plasmon dipole mode and trion, which is in the blue background region of Fig. 3(d) (r > 90 nm). This energy interval is still comparable with γ_X,T and smaller than (γ_pl + γ_T)/2, further implying that the hybrid system falls into the moderate coupling regime. We thus conclude that the dips in the scattering spectra of the hybrid system can be regarded as the Fano dips, a feature of moderate coupling, which arises from the coherent interaction between the discrete exciton (trion) state and the broadband of plasmon mode. Moreover, the crossing of the dispersion curves is found between the middle and lower energy branches when r < 90 nm, manifesting a relative weak coupling strength for the plasmon–trion interaction in this region. Of note, due to the photoinduced electron doping, the emission strength of the trion increases linearly with the excitation power.⁸ Thereby, for the hybrid system with the small-sized nanosphere, the plasmon–trion coupling could be enhanced by introducing another high-power control light.

The Fano resonance of the hybrid system combines the merits of the local field enhancement and the strong excitonic effect and therefore possesses an ability to greatly boost the PL radiative rate. In Fig. 4, we inspect the PL enhancement of the hybrid system under the excitation of a 532 nm laser. Figure 4(a) shows a representative enhanced PL spectrum for the hybrid system with r = 100 nm, which can be decomposed to an exciton and a trion emission with peak positions of 623 and 633 nm, respectively. Compared with the PL emission from the pristine WS₂ shown in Fig. 2(d), the redshifts of the exciton and trion are observed in the hybrid system. Possibly, it is resulted from the mechanical strain in monolayer WS₂ after depositing the Au nanosphere.⁴⁸ Another reason may lie in the plasmon resonance of the Au nanosphere generating energetic hot electrons, which inject into the monolayer WS₂ to produce the spectral shift of the exciton and trion as those have been reported in the literature.⁴⁹ Moreover, an 8.1-fold enhancement in the exciton peak intensity and a 3-fold enhancement in the trion peak intensity are observed, compared to the PL spectrum of the pristine monolayer WS₂ on the SiO₂/Si substrate [see the red curve of Fig. 2(d)]. From the electric field enhancement map in Fig. 1(c), it can be expected that the strong plasmon–emitter interaction occurs within the area beneath the nanosphere. Therefore, to eliminate background PL contribution, we define the PL enhancement factor as²³ 

where I_NS and I₀ are the PL peak intensities of the exciton and trion emitted from the WS₂ area with and without the nanosphere, A_NS denotes the area under the nanosphere (∼0.03 µm²), and A₀ represents the area of WS₂ we collected (∼4.91 µm²). By using Eq. (4), it yields from Fig. 4(a) that the PL enhancement factors for the exciton and trion emissions are 1265- and 680-folds, respectively. We summarize the PL enhancement factors for the exciton and trion as a function of the nanosphere radius, shown as the red dots in Figs. 4(b) and 4(c). It is suggested that with an increase in the nanosphere radii, the PL enhancement factors for both the exciton and trion have strong dependences on the nanosphere sizes and reach their maximum at r = 100 and 90 nm, respectively.

The spontaneous emission is dedicated by the photonic environment of the emitter through the local density of state (LDOS). The Au nanosphere on resonance can produce an increased LDOS that leads to the enhanced emission rate known as the Purcell effect. To further elucidate the PL enhancement observed in Figs. 4(b) and 4(c), we calculate the emission enhancement factor g_em for the exciton and trion using the finite-difference time-domain (FDTD) method [blue dots in Figs. 4(b) and 4(c)]. The evolution of g_em agrees well with that of the PL enhancement factor, indicating that the PL enhancement is dominated by the enhanced emission resulted from the plasmon mode. A discrepancy in the nanosphere radius for the maxima of g_em (r = 90 nm) and the PL enhancement factor (r = 100 nm) is also noted in Fig. 4(b). The reason may lie in the imperfect spherical shape for the Au nanosphere with r > 80 nm [see Fig. 3(b)], which gets elongated to be an ellipsoid, leading to a deviation in r. In addition, we calculate the LDOS maps of the nanosphere at the PL emission peaks of the exciton and trion. It can be seen from Figs. 4(d) and 4(e) that the LDOS of the exciton is larger than that of the trion, rendering a larger PL enhancement factor for the exciton emission as observed in Figs. 4(b) and 4(c).

In summary, we have developed a flexible method to manipulate both the plasmon–exciton and plasmon–trion couplings by integrating the monolayer WS₂ with the Au nanosphere. Due to the large exciton binding energy, strong resonance couplings between dipolar plasmon mode and the exciton (trion) are achieved at room temperature. The dispersions of these resonance couplings are measured by simply changing the radius of the nanosphere, rendering Rabi splittings of 89 and 48 meV for the plasmon–exciton and plasmon–trion couplings, respectively. These Rabi splittings manifest that the hybrid system falls into the moderate coupling regime, which combines the merits of plasmonic confinement and strong excitonic effect that greatly facilitates the PL enhancement of the monolayer WS₂. By inspecting the PL signal as a function of the nanosphere radius, it is found that 1265- and 680-folds of PL enhancements are realized for the exciton and trion emissions compared with those of the pristine monolayer WS₂ on the SiO₂/Si substrate. Our results provide a facile platform to manipulate the plasmon–exciton and plasmon–trion interactions at room temperature and could be beneficial to applications in atomically thin optoelectronic and nonlinear optical devices.

See the supplementary material for the dispersion of the plasmon dipolar mode in the Au nanosphere against the nanosphere radius (S1), the simulated scattering spectrum and charge distribution of the Au nanosphere (r = 100 nm) on the SiO₂/Si substrate (S2), the fitting parameters of the hybrid system for Eq. (1) (S3), the full view of bright-field and SEM images of the hybrid system (S4), and the optical setup for scattering and PL measurements (S5).

We gratefully acknowledge financial support from the National Key R & D Program of China (Grant No. 2017YFA0303800), the National Natural Science Foundation of China (NSFC) (Grant Nos. 11634010, 11874050, and 91950119), the Shaanxi Provincial Key R & D Program (Grant Nos. 2020JZ-10 and 2021KW-19), and the Fundamental Research Funds for the Central Universities (Grant Nos. 3102019JC008 and D5000210936). The authors would like to acknowledge the Analytical and Testing Center of Northwestern Polytechnical University for SEM measurements.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

The monolayer WS₂ was first identified with a microscope using the image contrast and was then confirmed by the Raman spectrum. The alumina layer was grown onto the monolayer WS₂ using the atomic layer deposition technique operating at 150 °C. The stock solution of Au nanospheres was diluted with deionized water at a volume ratio of 1:5 and then was spin-coated on the monolayer WS₂ to form the hybrid system (see Fig. S3 of the supplementary material). After the optical measurement, the radii of Au nanospheres were determined using the SEM images where the same nanospheres were retrieved by taking the edges of the WS₂ flake as the landmark [dashed lines in Fig. 2(b)].

The dark-field scattering spectrum of the hybrid system was obtained using a home-built dark-field confocal microscope (see Fig. S4 of the supplementary material).²⁰ A white light beam from a halogen lamp (Wyoptics, HL1000) was employed as the excitation with the polarization controlled using a Glan–Taylor polarizer. This white light beam was focused onto the sample through a 20× objective (Mitutoyo, NA = 0.4) at an incident angle of 60°. The scattering signal was collected by an upright 50× objective (Nikon, NA = 0.6) and then was recorded as the dark image using a CCD camera (STC-GEC33A, Sentech CO.). Meanwhile, the scattering light from the individual nanosphere is analyzed using the spectrometer (Shamrock SR-500i, Andor) equipped with an air-cooled CCD camera (iVac316-LDC-DD, Andor) and a blazed grating (150 lines/mm, blazed at 800 nm). After subtracting the background signal from the adjacent area, the record spectrum was adjusted against the spectral profile of the excitation to acquire the final scattering spectrum of the hybrid system. The PL measurement of the hybrid system was carried out on the same optical setup. A 532 nm continuous-wave laser with a power of ∼0.6 mW was focused onto the sample through a 150× objective (Leica, NA = 0.9). The diameter of the focused excitation beam is estimated to be ∼7.1 µm in the sample plane. The backscattered PL emission was collected by the same objective. After passing through a long-pass filter, the collected emission was directed to the spectrometer as that used in the scattering measurement. The data acquisition time for the scattering and PL spectra is 30 and 2 s, respectively. Notice that the Au nanosphere with the hybrid system is at least 2 µm away from other Au nanospheres and the WS₂ edge. To avoid the unwanted scattering and PL contributions, the scattered light from the single nanosphere was deterministically selected by spatially filtering optical signals through a pinhole.

The full wave simulations based on the FDTD method were used to calculate the optical responses of the hybrid system. The geometry of the hybrid system was modeled as the true values in the experiment. The permittivity of gold was taken from the experimental data of Johnson and Christy.⁵⁰ The refractive index of Al₂O₃ and CTAB was taken as a constant of 1.5 and 1.435, respectively. The permittivity of the WS₂ monolayer was taken from the previously reported experimental value.⁵¹ In the simulations, an s-polarized plane wave was used as the excitation, and the scattering spectrum was obtained by integrating the scattered electric field intensity over a virtual box enclosing the hybrid structure. The charge map of the nanosphere was derived by calculating the difference of the normal component of the electric field above and below the metal surface according to Gauss’s law.

To calculate the LDOS and the enhanced emission rate, the monochromatic electric dipole sources at peak wavelengths of the exciton and trion were used as the excitations in the FDTD simulation. Considering that the emission of monolayer WS₂ is dominated by the in-plane dipole, the dipole sources were placed beneath the Au nanosphere horizontally. After the raster scanning of the dipole source on a discrete grid (21 × 21), the LDOS maps were derived by a build-in command of the FDTD simulation. Since the emission rate is proportional to the LDOS, the emission enhancement factor g_em can be regarded as the ratio of the maximum LDOS with and without the nanosphere.²⁸