1. Introduction

A strong coupling between surface plasmon and the exciton is crucial in quantum optics [1–6], particularly in the application of nanofabrication technology for the design of quantum optical systems [7–9]. However, most of the current studies on strong coupling are based on a single exciton, and the composite structures in these experiments can only support two coherent states. Moreover, more coherent states can be formed if surface plasmon can achieve strong coupling using multiple excitons, which has great application potential in many frontiers of science and technology. A tunable plexcitonic material that sustains multimode hybridization is highly desirable, which is vital for advanced quantum devices. Therefore, the strong coupling between surface plasmon and multi-excitons is being widely studied [10]. Zhang W. et al. [11] constructed an Au nanocube@J-aggregates/monolayer WS₂ composite system by coating J-aggregates around an Au nanocube and placing it on a monolayer WS₂ surface. Further, they achieved diexcitonic strong coupling (DiSC) at room-temperature by adjusting the size of the Au nanocube. Similarly, Han X. et al. [12] constructed a composite system comprising an Ag nanocube and methylene blue (MB) dye. At low dye concentrations, strong coupling was realized between the Ag nanocube cube and single exciton. Additionally, double Rabi splitting was eventually achieved in the composite system as the dye concentration increased. Melnikau et al. [13] integrated Au@Ag core-shell nanorods and J-aggregates of two different dyes into a single hybrid structure, achieving collective exciton-plasmon coupling and dual-mode Rabi splitting by controlling the aspect ratio of the Au@Ag core-shell nanorods. Recently, Ye et al. [14] have recently reported the strong coupling between a plasmon mode and three different exciton states. Cuadra et al. [15] manipulated the charged and neutral excitons of single-layer tungsten disulfide (WS₂) to couple with the silver nanorods, forming a stable three-body hybrid plasmon-exciton-trions polariton state at low temperatures. These pioneering studies on strong coupling works using double excitons have successfully proved that three coherent states can be simultaneously formed in a nanocavity, providing a platform with more degrees of freedom for research on quantum mechanics. However, the double splitting coupling in room temperature between the double excitons generated by the spin orbit coupling of single-layer two-dimensional materials and the nanocavity has never been reported.

The energy diagram of double Rabi splitting is relatively complex, and the coupling between the double excitons and surface plasmon causes the formation of three energy branches as shown in Fig. 1. The high-energy branch is called the upper plasmon-exciton polariton branch (UP), the middle-energy branch is called the middle plasmon-exciton polariton branch (MP), and the low-energy branch is called the lower plasmon-exciton polariton branch (LP) [16,17]. In this study, the realization of double Rabi splitting between localized surface plasmon of single Ag@Au hollow nanocube and excitons in monolayer MoS₂ is reported. First, because Ag@Au hollow nanostructures can better localize electromagnetic fields compared with solid Au/Ag nanostructures [5,17], the mode volume is expected to be lower. Second, the properties of plasmon are affected by the change in the internal hollow structure [18–20]. Compared with solid Au/Ag nanostructures, Ag@Au hollow nanostructures can more conveniently realize the tuning of ${\lambda _{LSPR}}$ [21], thereby allowing the realization of strong coupling. Third, monolayer MoS₂ serves as an ideal platform for double exciton coupling. This platform is different from other multi-exciton coupling systems. It is capable of forming two stable excitonic states (A and B excitons) at room temperature. These unique excitonic states have been identified as direct excitonic transitions at the K-point of the Brillouin zone. The energy difference is due to the spin-orbit splitting of the valence band, which results in two resonances, the A and B exciton. They are obtained from the electrons in the valence band, which jump into the conduction band and form bound states with holes in the valence band owing to Coulomb interaction [22,23]. In summary, the two structures above were combined to form the Ag@Au HNC/MoS₂ composite system, which is expected to achieve strong coupling based on biexcitons.

 

Fig. 1. (a)Schematic diagram of energy level splitting owing to the strong coupling between the single Ag@Au HNC and monolayer MoS₂ composite structure. The top inset is the model diagram of the composite structure, and the bottom inset is the schematic of double Rabi splitting. (b) The dark-field microscope imaging of single Ag@Au HNCs. (c) The enlargement dark-field microscope imaging of single Ag@Au HNCs in (b). (d) The corresponding SEM images of the sample in (c). (e-h) The enlargement SEM images with scale length of 50 nm shown in (d).

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2. Experimental

Preparation of the Single HNC: First, relatively-homogeneous solid Ag nanocubes were prepared using a solvothermal synthesis method [24]. On this basis, a chemical reduction method [17] was used to continuously erode the silver atoms inside the solid Ag nanocubes by adding HAuCl₄, while depositing gold atoms on the outer surface of the Ag nanocubes. Secondly, a solution of Ag@Au hollow nanocubes was obtained. 10 ml of this solution was then centrifuged at a speed of 7000 r/min, and put into an ultrasonic machine for ultrasound at the maximum power to ensure that the particles in the solution are not aggregated. Finally, 15 $\mu l$ of the solution was dropped onto an ITO substrate, and the excess samples on the ITO substrate were washed away using ultra-pure water approximately 30 s later. In this way, a single Ag@Au HNC nanoparticle was obtained dispersed on the ITO substrate.

Preparation of a Hybrid Single Ag@Au HNC/Monolayer MoS₂: To prepare a single Ag@Au HNC/monolayer MoS₂ composite system, 15$\mu l$ of a solution containing Ag@Au HNCs was added to monolayer MoS₂ placed on an ITO substrate. The monolayer MoS₂ was purchased from SixCarbon Technology Shenzhen Co., Ltd. After the evaporation of the solution was completed, the composite system was observed and characterized using a dark-field scattering spectrometer and a scanning electron microscope (SEM).

Optical Characterization: In this study, the scattering spectra were measured using a dark-field microscope, and the SEM images were taken using a FEG QUANTA 650 SEM (FEI Inc., America). The optical measurements were all conducted at room temperature. An inverted dark-field microscope (Olympus IX71) was used, with unpolarized light from a halogen lamp passing through a dark-field condenser lens (N.A. = 1.2) and focused onto an ITO glass substrate. Scattered light was collected with a 100x objective lens (N.A. = 0.7). By focusing the scattered light from different nanostructures into the entrance slit of a spectrometer, spectra were obtained using a thermoelectrically cooled CCD.

To isolate single nanocubes, the sample solution concentration was first diluted to optimize the dispersion of individual particles. Solutions with varying concentrations were drop-cast onto plain ITO glass substrates and initially scaned with SEM(scanning electron microscope) to identify the best dilution for single isolated nanocubes.

To measure the dark field scattering spectrum of a single nanocube, we only placed one nanoparticle in the signal collection area of the spectrometer slit to avoid signal interference from other nanoparticles. Dark-field images of the corresponding single nanocubes were then taken with the optical microscope. After acquiring each spectrum, SEM was used to confirm the size of each single hollow nanoparticle.

3. Results and discussion

3.1 Scattering spectra analysis of single Ag@Au HNC

To realize the positioning observation of dark field microscope imaging and the spectral measurement of single Ag@Au HNC, the periodic coordinates on the ITO substrate were processed using electron beam etching. Fig. 1 shows the dark field optical imaging of Ag@Au HNCs on the labeled ITO substrate and the corresponding SEM images. It can be seen that the relative position relationship between the samples and coordinates can be clearly identified in the dark field image. In contrast to scanning electron microscope (SEM) imaging, the single Ag@Au HNC sample can be detected and its location can be recorded.

To detect the dark field scattering spectra of the single Ag@Au HNC, samples need to be dispersed as far as possible on the ITO substrate. For this purpose, the centrifugally-cleaned Ag@Au HNC solution was put in the ultrasonic cleaning machine for 10 min of ultrasound, before being dropped on the ITO substrate. After approximately 30 s, the excess samples on the ITO substrate were washed away using ultra-pure water. Fig. 2(a) shows the dark-field scattering spectra of the uncoupled Ag@Au HNCs, and the right side shows the SEM and dark-field microscope images corresponding to a-j, respectively. It can be seen that the color of the particles gradually changes from green to red with the change in the plasmon cavity mode of the single Ag@Au HNC and tuning of the dark field scattering spectrum (608 nm-724 nm). Thus, it is more conducive for the realization of double Rabi splitting.

 

Fig. 2. (a) Dark-field scattering spectrum of single Ag@Au hollow nanocubes (SEM images and dark-field microscope images corresponding to I-X are shown on the right inset, and the scale is 50 nm). (b) SEM image of the Ag@Au HNC/monolayer MoS₂ composite system on the ITO substrate (upper inset). The white dots represent Ag@Au HNCs. The lower inset shows the dark-field scattering image corresponding to the upper inset. The bright spots represent Ag@Au HNCs. The white broken line is the coverage boundary line of the substrate and monolayer MoS₂. The scale bar is 2 μm. (c) The solid lines i-ix represent the dark-field scattering spectra of a series of different single Ag@Au HNC and monolayer MoS₂ composite structures deposited on the ITO substrate. (d) The anticrossing diagram based on data extracted from (c). Double Rabi splittings are 90 meV and 120 meV respectively. The green, red, and blue points represent the UP, MP, and LP, respectively, and the corresponding solid line is the fitting result.

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3.2 PL spectrum analysis of monolayer MoS₂

The PL spectrum of monolayer MoS₂ on the ITO substrate was then measured excited by 532 nm laser (see the Supplement 1, Fig. S1). Two PL peaks can be observed at 610 nm (or 2.03 eV) and 660 nm (or 1.87 eV), corresponding to the B and A exciton peaks, respectively. These peaks are located within the tuning range (608-724 nm) of the scattering spectrum, which provides a high-quality platform for subsequent research on the strong coupling of double excitons in the Ag@Au HNC/monolayer MoS₂ composite structure.

3.3 Scattering spectrum analysis of single Ag@Au Hnc/monolayer MoS₂ composite structures

The prepared Ag@Au HNCs samples can be freely tuned in the range of 608-724 nm overlapping the two PL peaks at 610 nm and 660 nm of monolayer MoS₂, which provides the possibility for studying the strong coupling between surface plasmon and double excitons. Therefore, the single Ag@Au HNC/monolayer MoS₂ composite structure was constructed, and the strong coupling properties of this structure were studied at room temperature. Fig. 2(b) shows the SEM and dark-field microscope images of coupled Ag@Au HNCs/monolayer MoS₂ composite structure. Fig. 2(c) shows the scattering spectra of the Ag@Au HNC/monolayer MoS₂ composite structure with different sizes as shown in Fig. 2(b). The spectra show evident depressions at the A and B exciton peaks of the monolayer MoS₂, which split into three new surface plasmon-exciton resonance peaks. The results show that the surface plasmon interacts with the double excitons of monolayer MoS₂ to form three new states: UP, MP, and LP. In addition, more obvious experimental results showing in the Supplement 1, Fig. S2. Furthermore, fitting the energy of the three branches of the composite structure after spectral splitting, to draw the anticrossing curve of the strong coupling system not only helps in highlighting the characteristics of strong coupling, but also serves as strong evidence [13,15, 25] of strong coupling between surface plasmon and exciton. The coupled oscillator model (COM) mode was used to fitting and analyze the experimental results, the COM model [26,27], provides a very good fit of the data. As shown in Fig. 2(d), two distinct anticrossings are observed at both excitons resonances, and large double Rabi splittings (90 meV and 120 meV) are obtained successfully. The green, red, and blue dots, respectively correspond to the three peaks of each spectrum in Fig. 2(c)); the solid lines indicate the UP, MP, and LP branches after Lorentz fitting; and the green, yellow, and black dotted lines, respectively, indicate the A and B exciton energy of monolayer MoS₂, and the surface plasmon energy of uncoupled single Ag@Au HNC. The results show that the trajectories of all peaks have a double anticrossing relation, which is a typical characteristic of the strong coupling between surface plasmon and diexcitonic [11,12].

3.4 FDTD simulations

To verify the correctness of the experiment, the FDTD simulation were performed in this study. The perfectly matched layer (PML) which can absorb all transmitted electromagnetic waves and effectively avoid the influence caused by boundary reflection, was set as the boundary condition [28]. When modeling the structure of a single Ag@Au HNC/monolayer MoS₂, the monolayer MoS₂ is represented as a dispersive dielectric layer with a thickness of 0.7 nm, and the mesh was set 0.1 nm to overrided the materials region. The dielectric permittivity of monolayer MoS₂, which is based on in-plane optical constants, is derived from the referenced literature [29,30]. Johnson-Christy medium data were used for both Au and Ag, and an air medium with a refractive index of 1 was used for the hollow part. The model was placed in the x-y plane along the x direction. The adjustment of the thicknesses of the Au and Ag shells is based on high-resolution TEM measurements (see the Supplement 1, Fig. S3 and Fig. S4), which provide precise and detailed insights into the structures of these materials. The ${\lambda _{LSPR}}$ redshift (565nm-701 nm) of the single Ag@Au HNC was achieved by slightly adjusting the thickness of the Au (5-20 nm) and Ag shells (15-0 nm), as shown in Fig. 3(a) i-xvi.

 

Fig. 3. (a) The scattering spectrum is tuned by changing the shell thickness of a single Ag@Au HNC. The side length of the HNS is 87 nm, the shell thickness and the resonance peak postions in (a) of the core-shell structure from line xvi-i are 18 nm (598 nm) [shell thickness, nm (resonance wavelength)], 14(606), 13.8(609), 12.5(614), 11(625), 10.8(628), 10(640), 9.5(649), 9(655), 8.6(661), 8(680), 7.4(684), 7(693), 6.9 (696), 6.66(707), 6(722), respectively. (b) Simulated scattering spectra of a single Ag@Au HNC and monolayer MoS₂ composite structure corresponding to (a). (c) The data extracted from (b) is drawn to obtain the anticrossing relationship, where the green, red, and blue points represent the UP, MP, and LP, respectively; and the corresponding solid line is the fitting result. (d) Schematic diagram of energy level splitting in owing to the strong coupling between the single Ag@Au HNC and monolayer MoS₂ composite structure.

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This indicates that the local surface plasmon (LSP) mode of Ag@Au HNC has high sensitivity to thickness of the shell. Furthermore, the single Ag@Au HNC/monolayer MoS₂ composite structure was formed by placing the monolayer MoS₂ between a single Ag@Au HNC and the ITO substrate. It can be seen from Fig. 3(b) that when the ${\lambda _{LSPR}}$ of the single Ag@Au HNC is close to the A and B exciton peaks of the monolayer MoS₂, the scattering spectrum of the composite structure has evident depressions at both exciton peaks. Simultaneously, three new surface plasmon-exciton resonance peaks are formed, which indicates that diexcitonic splitting has occurred. To intuitively reflect the interaction of the composite structure, the data on the three resonance peaks in Fig. 3(b) were extracted, and the anticrossing relationship was drawn, as shown in Fig. 3(c), where the results are highly consistent with the experimental results.

Subsequently, the mode volume of the Ag@Au HNCs in the system were calculated using the following formula [26,31,32]:

As shown in Table 1, the effective mode volume of Ag@Au HNCs with a ${\lambda _{LSPR}}$ of 660 nm is 88, 786 nm³, which is much smaller than that of solid Au/Ag nanocubes with the same absorption peak position, further proving that Ag@Au HNCs provide a high-quality platform for studying surface plasmon-biexcitonic strong coupling. Simultaneously, calculated electric field distributions of Ag@Au HNC, solid Ag@Au NC, solid Au nanocubes and solid Ag nanocubes at the same resonance wavelength (660 nm), we observed that the maximum electric field in the gap region between the HNC and the substrate is twice that of the other nanopartical and the substrate at the same resonant peak. Which also shows that Ag@Au HNC has a stronger electromagnetic field confinement capability than the other nanostructures. Fig. S5(e) shows the simulated scattering spectra of four different structures (Ag@Au HNC; Ag@Au NC; Au NC; Ag NC) at the same resonance wavelength (660 nm). It can be seen that among the four structures, the Ag@Au HNC shows a narrower half-peak width of height (FWHM) in the scattering spectra, so the quality factor of the hollow nanoparticle cavity is higher. According to the strong-coupling figure of merit ${Q / {{V^{1/2}}}}$ [32]. The higher quality factor Q and the smaller mode volume of the hollow nanoparticle cavity collectively highlight the advantage of HNC in achieving strong coupling (see the Supplement 1, Fig. S5).

Table 1. LSP mode volumes of different types of nanocubes at 660 nm.

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3.5 Theoretical analysis

Based on the above experimental and simulation results, the three new resonance peaks of the proposed composite structure present a double anticrossing relationship, which is a typical characteristic of the strong coupling between surface plasmon and diexciton [33–35]. To describe the anticrossing relationship in the composite structure, we further use three coupled harmonic oscillator models were used to describe the system [36–40]:

Through diagonalization, $\omega$ has three solutions corresponding to green, red and blue line in the energy level diagram reflected in Fig. 3(d). When the ${\lambda _{LSPR}}$ of the single Ag@Au HNC is located near the exciton peaks of monolayer MoS₂, the composite structure exhibits an unusual spectral splitting phenomenon due to the exciton peaks of monolayer MoS₂, and the composite structure shows three splitting peaks. thus, the composite structure contains three new resonance peaks, corresponding to UP, MP, and LP, respectively. Moreover, the Rabi splitting energies of the surface plasmon and A and B excitons at zero tuning (${\delta _A} = {\omega _p} - {\omega _e}A = 0$, ${\delta _B} = {\omega _p} - {\omega _e}B = 0$) are $\hbar {\Omega _{ML}} = 105$meV, and $\hbar {\Omega _{UM}} = 119$meV, respectively, as shown in Fig. 3(c).

We use the strong coupling criteria mentioned in the literature [5,42,43] as follows:

Here, g is the coupling strength, $\kappa$ and $\gamma$ denote the decay rates of the uncoupled surface plasmon and the two A and B excitons, respectively. In our system, the plasmon linewidth of the HNC can be extracted from the scattering spectrum of a single HNC as 240 meV, the monolayer MoS₂ was extracted to be 50 meV and 95 meV for the A (1.87 eV) and B (2.03 eV) exction, respectively. We use the scattering expression derived from the coupled oscillator model to fit spectrum in Fig. 2(c) and obtain a coupling strength g of 90 meV and 120 meV, which both satisfies the SC criterion of Equ. (3).

4. Conclusions

In summary, a composite structure comprising a single Ag@Au HNC/monolayer MoS₂ was constructed on a clean ITO substrate and its scattering spectrum was measured. The experimental results show that the scattering spectra exhibit a clear depression at both the A and B exciton peaks of the monolayer MoS₂, which split to form three new resonance peaks. In the plotted curves, the trajectories of all peaks showed a double anti-crossing relationship, which is typical for strong coupling between surface plasmon and biexcitons. The scattering spectra of the composite structure were then simulated using the FDTD method, and the phenomena agreed well with the experimental results. Simultaneously, the mode volume of Ag@Au hollow nanocubes was calculated and found to be significantly smaller than that of solid Ag/Au nanocubes at the same scattering peak. In this study, we have realized the double splitting coupling in room temperature between the double excitons generated by the spin orbit coupling of single-layer two-dimensional materials and the nanocavity has never been reported. This research provided a new structural system for realizing strong coupling based on two-dimensional materials.