Quantifying photoinduced carriers transport in exciton–polariton coupling of MoS2 monolayers

Exciton–polariton coupling between transition metal dichalcogenide (TMD) monolayer and plasmonic nanostructures generates additional states that are rich in physics, gaining significant attention in recent years. In exciton–polariton coupling, the understanding of electronic-energy exchange in Rabi splitting is critical. The typical structures that have been adopted to study the coupling are “TMD monolayers embedded in a metallic-nanoparticle-on-mirror (NPoM) system.” However, the exciton orientations are not parallel to the induced dipole direction of the NPoM system, which leads to inefficient coupling. Our proposed one-dimensional plasmonic nanogrooves (NGs) can align the MoS2 monolayers’ exciton orientation and plasmon polaritons in parallel, which addresses the aforementioned issue. In addition, we clearly reveal the maximum surface potential (SP) change on intermediate coupled sample by the photo-excitation caused by the carrier rearrangement. As a result, a significant Rabi splitting (65 meV) at room temperature is demonstrated. Furthermore, we attribute the photoluminescence enhancement to the parallel exciton–polariton interactions.


INTRODUCTION
Strong light-matter interactions exhibit many compelling features, owing to their potential applications in low-threshold lasing 1,2 , Bose-Einstein condensate 3,4 , and superfluidity 5,6 . These approaches are generally employed using a single emitter and resonant cavity. Furthermore, a strong coupling occurs when the energy-exchange rate exceeds both the emitter scattering rate γ and cavity dissipation rate ĸ. Upon achieving a strong-coupling regime, a new hybrid eigenstate is formed because of the energydifference-induced splitting of two polaritonic states. This phenomenon is known as vacuum Rabi splitting. To achieve a strong-coupling regime, the coupling strength g should be greater than (γ, ĸ)/2 7 . In addition, the intermediate coupling regime is γ > 2 g > ĸ, which has caught some attention lately 8,9 . Therefore, selecting an appropriate emitter and cavity is crucial in such hybrid systems. Thus far, several strong-coupling systems have been demonstrated with dye molecules [10][11][12] or quantum dots [13][14][15] as emitters; these conventional platforms have high Rabi splitting energies. Additionally, dye molecules can be easily photobleached, and quantum dots are prone to oxidization and agglomeration, both of which hinder their further applications.
Two-dimensional (2D) transition metal dichalcogenide (TMD) semiconductors with structures MX 2 , where M is Mo or W and X is S, Se, or Te, have introduced many possibilities in photonics because of their remarkable optical and electronic properties. When the layer number of TMDs is reduced to monolayers, a transition from indirect to direct bandgap semiconductor occurs 16,17 . TMD monolayers have generated significant interest because their excitons can operate in the visible to near-IR regions. Additionally, the excitons are stable at room temperature. Importantly, the exciton binding energies of TMD monolayers (e.g., 240 meV 18 for MoS 2 , and 700 meV 19 for WS 2 ) are significantly higher than γ (γ~k B T = 26 meV) at room temperature. Because of the above-mentioned advantages, TMDs are appropriate emitters for developing strong-coupling systems.
Additionally, the cavity dissipation rate is critical for the coupling strength. To achieve energy-exchange cycle between the cavities and emitters, a low cavity dissipation rate is required; the rate is inversely proportional to the quality factor Q, i.e., κ∝1/Q. Various types of cavities such as photonic-crystal cavities 20 , microcavities 21 , and Fabry−Peŕot cavities 22 were developed to facilitate strong coupling in TMDs. Because the coupling strength varies as g / ffiffiffiffiffiffiffiffi 1=V p , where V denotes the effective cavity mode volume 11 ; a significantly small cavity mode volume and high-Q resonator are favorable. Accordingly, plasmonic cavities are desirable because of their deep-subwavelength mode volumes. Many recent reports have adopted exciton-plasmon coupling systems that have the metallic-nanoparticle-on-mirror (NPoM) structure, in which TMDs are placed between the metal nanoparticles and mirror 9,23,24 . When an NPoM system is optically illuminated, the gap plasmon mode provides significant electricfield confinement and ultra-small mode volume 11 . However, the strong localized field in NPoM systems is primarily out-of-plane and cannot satisfactorily couple with the in-plane exciton dipole of TMDs 23,25 . Therefore, we propose Au nanogroove (NG) arrays, on the top of which we place MoS 2 monolayers; the strongly localized electric field of Au NGs is parallel to the in-plane exciton dipole of MoS 2 monolayers.
Such exciton-polariton coupling systems with high splitting energy result in a significant reconstruction of the energy levels of the system. To explore the electronic-energy transfer in exciton-polariton coupling systems, the surface potential (SP) 1 change is a crucial evidence. It has been reported 26 that the WF changes the organic material-cavity strong-coupling system. The highest occupied-orbital-lowest-unoccupied-orbital transition in a photochromic spiropyran-doped polymer results in the electronicenergy transfer owing to strong coupling. However, the strong coupling can occur in the absence of light and exchange the coherent energy as mentioned above. The photo-excited bandgap of MoS 2 can excite carriers and induce the electric field of Au NG which cause carrier rearrangement in the exciton-polariton coupling system 27 . The coherent energy exchange between excitons and plasmons in the strong-coupling regime and intermediate coupling can promote charge transfer which has been discussed using far-field pump-probe measurements 27,28 . However, far-field pump-probe measurements cannot provide the evidence of couplings in the nanoscale. By using Kelvin probe force microscopy (KPFM) equipped with a light source, one can calculate the photoinduced SP change of the sample by measuring the surface potential difference (SPD) between the scanning probe and samples at the nanoscale.
In this study, we propose 1D plasmonic NG arrays and incorporate them with 2D MoS 2 , which demonstrates a significant Rabi splitting (65 meV) at room temperature. The electric-field distribution clearly reveals the coupling between the NG plasmonic mode and exciton mode. Additionally, the photoexcited carrier transfer from MoS 2 can be facilitated by coherent energy exchange, and the parallel exciton-polariton enhanced the interaction that revealed in the SP change. Many instances of photoluminescence (PL) intensity enhancement were observed. Our findings are important basis to further study the TMD-plasmon coupling.

RESULTS AND DISCUSSION
Strong coupling in MoS 2 monolayers on 1D plasmonic NGs Figure 1a depicts a two-level system with the ground state (|g〉) and excited state (|e〉) separated by ћω bg , which denotes the coupling of a 2D material exciton with an NG cavity. When the energy-exchange rate Ω is higher than the decay rate (γ, ĸ) of this system, two polaritonic states (upper polariton branch (UPB) and lower polariton branch (LPB)) are formed, which are separated by Rabi splitting. In this study, wafer-scale MoS 2 monolayers were grown using the vapor-liquid-solid method 29,30 . The characteristics of the MoS 2 monolayers were confirmed via Ramanspectroscopy measurements, as depicted in Fig. 1a. As previously reported [31][32][33] , the layer number can be identified by the frequency difference between the E 1 2g and A 1g modes. Figure 1c depicts the PL spectra of the MoS 2 monolayers excited using a 532 nm continuum-wave (CW) laser, which shows exciton emission at 675 nm (1.84 eV).
To characterize exciton-polariton coupling features, we employed Au NG arrays as optical cavities and transferred the MoS 2 monolayers on their top, as depicted in Fig. 2a. Such plasmonic nanostructures of surface plasmon resonances (SPRs) can be controlled by adjusting the geometry size, and the degree a Exciton-polariton coupling system between a plasmonic cavity with a resonant ω p and TMD excitons. In this system, the parameters that determine the coupling strength are the energy-exchange rate Ω, cavity loss rate γ, and emitter loss rate κ. The right panel depicts the energy diagram of the strong coupling of the 2D TMD semiconductor with a direct bandgap ћω bg between the ground state |g〉 and excited state |e〉 coupled to the plasmonic-cavity mode ћω p . The coherent coupling forms a hybrid state with UPB and LPB separated by Rabi splitting energy ћω R . b The Raman spectra of the MoS 2 monolayers after being transferred on the Au film. The frequency difference between the E 1 2g and A 1g modes is 19.81 cm -1 , which indicates monolayers. c PL spectra of the MoS 2 monolayers.
of enhancement can also be utilized to study the strong coupling. Au NGs 34,35 generate a strongly local field, which is dominantly in plane; in this field, effective coupling occurs between the NGs and MoS 2 (see Fig. 2b). The NGs were fabricated via focused-ion-beam milling on a 150-nm-thick Au film ( Supplementary Fig. 1). Their SPR wavelength can be easily tuned by precisely controlling the NG depth, allowing the adjustment of the SPR wavelength to match the exciton energy of the MoS 2 monolayers. Figure 2c depicts a single-plasmonic mode with individual NGs of various depths which are in the range of 55-105 nm. After integrating the MoS 2 monolayers , a splitting between exciton-plasmon polariton (or plexcitons) was observed in the reflectance spectra (see Fig.  2d). The simulated spectra depicted in Supplementary Fig. 2 was obtained by varying the depth of NG.
In order to determine whether this hybrid system is strongly coupled, we adopted a classical model that predicts UPB and LPB in agreement with the quantum-mechanical Jaynes-Cummings model as 8,11,23 where E ± represents UPB (+) and LPB (-), as depicted in Fig. 3a; E p and E 0 denote the energy of the pure plasmon-cavity mode and MoS 2 exciton energy, respectively; and δ = E p −E 0 denotes the detuning energy between plasmon and exciton. Although the thickness of each MoS 2 monolayer is approximately 0.6 nm, the SPRs are sensitive to the change in the surrounding refractive index. Therefore, we red-shifted approximately 26 nm from Fig. 2c, d without considering the coupling effect to obtain a more accurate fitting curve. The coupling strength, as a function of cavity and exciton, can be described as 8,11,23,24 where μ e , N, and V denote the exciton-transition dipole moment, number of excitons coupled to the cavity, and mode volume of the cavity, respectively. The intermediate coupling regime was observed with the Rabi splitting energy of 65 meV which is comparable with the excitonic linewidth but smaller than the plasmon linewidth 8,9 . By simulating the 2D contour plot depicted in Fig. 3b, an anticrossing behavior was observed. To numerically understand the MoS 2 /NG coupling system, we used a commercial finite-difference time-domain (FDTD) software program (Lumerical) to calculate the Purcell factor F p ¼ 3 which describes the enhancement of the spontaneous emission rates of atoms when they integrate into a cavity. In our Au NG nanocavities, F p % 4:03 10 4 , in which the effective mode volume was calculated to be 78 nm 3 (Supplementary Fig. 3). Moreover, we have listed the strong coupling in TMDs from recent works in Supplementary Table 1. To the best of our knowledge, we have observed the largest Rabi splitting among all the works on MoS 2 at room temperature, and the splitting is even comparable to that at the low temperature of 77 K 36 . The large Rabi splitting is attributed to 1D plasmonic NGs, which can excite plasmonic mode parallel to the in-plane TMD excitons. As discussed in the "Introduction" section, this cannot be achieved via plasmonic NPoM cavities, thereby highlighting the advantage of using 1D plasmonic NGs.

Photo-excited carriers in an intermediate coupling system
In KPFM-based study, the SPD can be obtained using the contact potential difference (CPD) between the probe and samples. In KPFM measurement, the increase and decrease in the SP indicates the accumulation of electrons and holes. To further understand the electronic-energy transfer process that occurs upon photoexcited carriers in the exciton-polariton coupling system, KPFMbased studies can be a crucial evidence (see Fig. 4). The SPD was measured on the same NG arrays by tuning the 532 nm laser on and off during the scanning. Therefore, the SPD that occurred upon illumination with 532 nm light is written as As a control, a MoS 2 /Au film was measured in the same measurement conditions. Another interesting feature in strongcoupling system is that it occurs even in the absence of light. Therefore, we excited MoS 2 exciton to observe carriers' transfer in the intermediate coupling system. Figure 4a illustrates the electronic energy transfer process. While the photon energy is greater than MoS 2 monolayers bandgap, the electron can be moved into the excited state and transferred to Au NG through the Rabi splitting channel. Figure 4d    indicates that the SPD is proportional to 1/detuning. However, the SP of MoS 2 on Au film did not respond to the laser illumination, because the thickness of MoS 2 monolayers is too thin and caused electron-hole pairs to accumulate at the MoS 2 -Au interface, resulting in neutral SP. The quantitative calculation of electron densities in MoS 2 monolayers at various detuning levels are shown in Supplementary Fig. 4. At a detuning of~23 meV, the electron density in MoS 2 is decreased to 3.22 × 10 12 cm −2 , which can be attributed to MoS 2 carriers transferred to Au NGs. Therefore, it is clear that the measured SPD changes are induced by the intermediate coupling system.

PL enhanced via high Purcell factor
For the on-coupling sample (MoS 2 /NG3), the excitons almost overlapped with the SPR, indicating significant PL enhancement, as depicted in Fig. 5. The plasmon-assisted PL-enhancement factor (EF) is determined as 37,38 EF where E and η denote the electric-field intensity and quantum yield, respectively, and the symbol with and without the "singleprime" represent with and without Au NG, respectively. The MoS 2 spontaneous emission rate of excitons in the hybrid system will be significantly fast because the SPR results in new radiative pathways. According to the Fermi's golden rule, the transition rate is proportional to the photonic density of states. Therefore, the PL EF can be simplified as Moreover, MoS 2 incorporated with plasmonic cavities can tailor the luminescence spectra in terms of emission-intensity enhancement, peak position, and shape modification as also shown in Table 1, three of which have been widely studied [39][40][41] . When strong coupling occurs, the exciton-plasmon energy-exchange rate is higher than the radiative and non-radiative rates of excitons. Conversely, the energy is transferred from excitons to plasmons, and the excitons are then re-excited via the collective electron oscillation of plasmons in a strongly localized electric field. To characterize the relation between intermediate coupling and PL, the Purcell-factor calculations of on-coupling and offcoupling samples are listed in Table 1. The on-coupling sample with a high Purcell factor has high electromagnetic-fieldconfinement ability, which can assist in modifying the PL intensity and lifetime. Our demonstration of the photo-excited carriers in the intermediate coupling with MoS 2 monolayers on the proposed plasmonic metasurfaces was demonstrated only by photoexcitation. Since optically induced exciton-polariton coupling happens at the sub-100 femtosecond 28 , our finding suggests the promising future of ultrafast plasmonic switches, by integrating 2D material with proposed plasmonic metasurfaces.
We successfully demonstrated that MoS 2 monolayers on top of 1D plasmonic NGs could achieve intermediate coupling at room temperature. The key feature of our structure was that the plasmonic fields and excitons were in parallel. The anticrossing curve revealed the Rabi splitting energy was approximately 65 meV, which is comparable with the excitonic linewidth but smaller than plasmon linewidth, confirming the intermediate coupling. The SP change that occurred upon photo-excited carriers' rearrangement was attributed to MoS 2 bandgap excitation and the induced hot-electron (hole) in Au NG. The observation of electronic energy exchange versus detuning of the plasmon resonance provides the evidence that the electronic equilibrium breaking via photo-excitation in the intermediate coupling system. The intermediate coupling phenomenon can also modify the PL intensity of the excitons. All the results confirmed that TMD-loaded 1D plasmonic NGs are ideal platforms to study the exciton-plasmon interaction. The findings of this study could initiate the development of various optoelectronic applications, such as low-threshold lasers and integrated plexciton devices. This work can provide a great potential for improving the performance of metal-2D semiconductor heterodevices in the field involving photoconversion.

Growth and transfer of MoS 2 -monolayer film
We performed salt-assisted CVD 29,30 to synthesize a monolayer MoS 2 film. First, 2 mg/ml aqueous solution of Na 2 MoO 4 (T m = 687°C) was spin-coated on a sapphire substrate. Subsequently, the substrate was loaded in the center of the CVD chamber (a quartz tube; length: 1 m; diameter: 2 in). Approximately 100 mg of sulfur was loaded in the upstream of the

Fabrication of Au NG arrays
First, 150-nm-thick gold films were deposited on silicon substrates using an electron-gun evaporation system. The NGs were then milled using a focused-ion-beam system (DB-FIB, FEI Helios NanoLab G3 CX, NCKU, Taiwan) under the acceleration voltage of 30 kV and ion beam current of 24 pA. The depths of the NGs were precisely controlled via dose adjustment.

Optical measurement
A confocal microscope (WITec Alpha 300S, Ulm, Germany) with a halogen lamp was used to measure the reflectance of the Au NGs. A 20× objective lens (Olympus) with a numerical aperture (NA) of 0.25 was used to collect the reflectance signal, which was recorded using a spectrometer (Acton SP2300, Princeton Instruments). In Raman-spectroscopy and PL measurements, the samples were excited using a 532 nm Nd:YAG CW laser at 0.8 mW to avoid sample damage. The Raman and PL signals were investigated using a 50× objective lens (Olympus, MPlanFL) with an NA of 0.8. Additionally, a 532 nm notch filter was used to block the excited signal, which was resolved using a 600 g/ mm diffraction grating and recorded using a spectrometer (Acton SP2300, Princeton Instruments).

KPFM measurement
The sample was mounted on an apparatus stage and electrically contacted to the ground. The SP difference was observed via KPFM using an atomic force microscope (TT-2, AFM Workshop) with SP measurement (SPT-20, Toyo Corporation). The probe was equipped with a Pt-coated tip at a frequency of approximately 70 kHz in the non-contact mode. In the SPT-20 setting, the alternating current bias, V ac , applied 1 V at a frequency of 39 kHz to the probe.

Simulation
The FDTD method was employed to calculate the reflectance spectra, electric-field distribution, and Purcell factor by using a simulation software from Lumerical. In this modeling, the shapes of the Au NGs are same as the SEM cross-section images and were placed on the silicon substrate. The MoS 2 monolayers were then placed on top of the Au NGs, and the thickness of each monolayer was 0.6 nm. The wavelength-dependent refractive indices of Au and monolayer MoS 2 were as given in Johnson and Christy 42 and Jung et al. 43 , respectively. Notably, x-polarized plane waves were used to illuminate the Au NGs and MoS 2 /Au systems. In Purcell-factor calculation, an x-polarized dipole source was placed at the center of the MoS 2 monolayers to obtain the Purcell factor.