1. Introduction

Transition metal dichalcogenides (TMDs), consisted of stacked layers, have received much attention for a long period of time. Research about the electronic states, excitons and oscillator strength of TMDs has exhibited a variety of interesting phenomena [1–4 ]. Recently, the mono or few layers of TMDs were successfully obtained by mechanical exfoliation or chemical syntheses, which opened up the renaissance of layered TMDs. Layer dependence of the bandgap of TMDs has been clearly demonstrated, when the thickness reduces to few layers or even monolayer, the bandgap is greatly modulated and transform from indirect to direct [5–7 ], resulting in new opportunities for fundamental physical research and device applications. Considering of their relatively high charge carrier mobility [8] and tightly bound excitons [9,10 ], few layers TMDs were expected to be promising materials applied in optoelectronics. In recent years, a variety of TMDs-based optoelectronic devices including field effect transistors, LEDs, photo detectors, lasers and solar cells have been fabricated and their performance have been demonstrated [11–15 ]. Among TMDs, WS₂ is one of the intensively studied layered material and many novel exciton properties were reported. For example, the A- and B-exciton of WS₂ arise from the interlayer interactions and spin-orbit splitting [16], the magnitude of A-B splitting is independent of the number of layers [17], and a giant two-photon absorption effect supported by excitons [18]. Besides, in monolayer WS₂, the binding energy of the A exciton is huge enough [19,20 ], which provides an ideal platform for studying the exciton-related light-matter coupling effect.

In last decade, Exciton-photon strong coupling in semiconductors has also harvested much attention [21,22 ]. The strong coupling between excitons and photons would lead to new quasi-particles, i.e. exciton polaritons, generated. The unique properties of exciton polaritons were tremendously studied and some great advances have been achieved, such as, polariton lasing [23], Bose-Einstein condensation (BEC) of polaritons [24] and slow light [25], etc. Room temperature operation of polariton-based system is highly required for the real applications, thus large exciton binding energy and oscillator strength are necessary for semiconductors. Fortunately, the layered TMDs, exhibiting bandgaps ranging from the visible to near-infrared, large exciton binding energy and strong oscillator strength, would inject fresh vitality into the study of strong light-matter coupling. In 2014, by incorporating monolayer of molybdenum disulphide (MoS₂) into distributed Bragg reflector (DBR) mirrors, X. Liu et al. first reported room temperature 2D exciton polaritons with a Rabi splitting of 46 meV [26]. The strong coupling of exciton-cavity modes in MoSe₂/hBN hetero-structure tunable micro-cavity was reported just recently [27]. In theory, the high-temperature BEC in MoSe₂ sandwiched 3D photonic crystal bandgap materials [28], a semi-classical analysis of exciton-polaritons in TMDs and their direct excitation by energy transfer from proximal electric dipole emitters were also reported, respectively [29]. 2D excitons in monolayer have themselves properties including enhanced photoluminescence efficiency, larger binding energy, which are favorable for strong exciton-photon coupling. However, some intrinsic properties of excitons and band structures can be traced from bulk materials [30], thus to a fuller understanding of the fundamental properties of exciton polaritons in the layered materials, the study of excitons coupled with light in multi-layers or bulk TMDs are highly desirable. The research may provide new viewpoints or inspirations for the strong coupling effect in layered materials.

In this work, we focused on the strong coupling effect between excitons and Fabry-Pérot (F-P) micro-cavity in multi-layered WS₂ flakes. To avoid the complicated fabrication process of DBR, we tactfully take advantage of high dielectric constant of WS₂ [31], self-constructed F-P micro-cavity is formed between top and bottom surfaces of WS₂ flakes. By measuring the micro-reflectance of WS₂ flakes with different thickness, we successfully observed the anti-crossing behavior of strong coupling between excitons and cavity modes. The giant Rabi splitting of A- and B-exciton were evaluated to be ~270 meV and ~780 meV, respectively, which are much larger than that of polariton in monolayer.

2. Experimental details

The WS₂ flakes were mechanically exfoliated from bulk crystals and transferred on SiO₂/Si substrates. By using atomic force microscopy (AFM) in tapping mode, WS₂ flakes with thickness ranging from 20 to 80 nm were chosen. A home-made micro-reflection system, shown in Fig. 1(a) , was built to measure reflectance spectra on these flakes with size of just several micrometers. With the help of field stop (FP) at real image in our system, light from the background was suppressed and sub-μm spatial resolution was achieved. In order to observe clear excitons’ features and the variation of optical properties with different thickness, the samples were cooled to 77K in a cryostat. The illumination source used in the measurements was 10-250 W tunable Quartz Tungsten Halogen lamps (Newport 66884 Research QTH Lamp), and the reflectance signals were gathered by grating spectrometer equipped with CCD (JY Horiba iHR 320). Furthermore, the Raman spectra of WS₂ flakes were measured by a Raman system (JY Horiba LabRam HR800 Ev) with 532 nm excitation laser.

 

Fig. 1 (a) Schematic of experimental set-up for micro-reflectance measurements. The illuminating light passes through a beam splitter (BS) to enter a microscope and then focuses on samples. Field stop (FP) is introduced to reduce the signal from background. (b) Optical image of a WS₂ thin flake. (c) AFM image of the flake on SiO₂/Si, with a thickness of 32 nm. (d) Raman spectra with excitation wavelength of 532 nm. The inset gives Raman spectra of mono-layer, 32 nm and bulk WS₂, respectively.

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3. Results and discussion

The typical optical image of a WS₂ flake is present in Fig. 1(b). AFM image shows that the flake has a uniform height of around 32 nm, as illustrated in Fig. 1(c). To determine the structural properties of the flake, of which the thickness is in a range of several tens of nanometers, Raman measurement was conducted and the spectrum is shown in Fig. 1(d). Because the excitation wavelength is near resonant with B exciton of WS₂, there exists abundant Raman mode both in lower and higher wavenumbers [32]. By using multi-peak Lorentzian fitting, we separated their respective contributions and presented them by red curves in Fig. 1(d). The first-order mode at the Brillouin zone center ($E_{2\text{g}}^1\left(\Gamma \right)$and$A_{1g}\left(\Gamma \right)$) were extracted at 357.5 and 421.8 cm⁻¹, respectively. Comparing the values of monolayer (357.713 and 418.157 cm⁻¹) and bulk WS₂ (357.3 and 421.8 cm⁻¹), which are presented in the inset of Fig. 1(d), we confirmed that the WS₂ flakes with thickness of tens nanometers are very close to bulk material. Moreover, it can be seen clearly that the $E_{2\text{g}}^1\left(\Gamma \right)$ mode red-shifts with the increasing of thickness and $A_{1g}\left(\Gamma \right)$ mode blue-shifts. It is consistent with the former reports [33,34 ], which verified that the red-shift of $E_{2\text{g}}^1\left(\Gamma \right)$ is caused by an enhancement of the dielectric screening of the long-range Coulomb interaction between the effective charges, and the blue-shift of $A_{1g}\left(\Gamma \right)$ is ascribed to the increasing of the restoring force originating from Van der Waals interactions between the layers.

As we have mentioned above, it is expected that self-constructed F-P type micro-cavity, benefited from very high dielectric constant of WS₂, can be formed between top and bottom surfaces of the WS₂ flake by selecting suitable thickness. To prove it, three samples with different thickness (25 nm, 54 nm and 70 nm) are prepared and characterized through our home-made micro-reflectance technique. As shown in Fig. 2 , different spectral features of the three samples are clearly observable. When the thickness(d) is 25 nm, only two reflection minima(I, II) in reflectance are observed in 2.05 eV and 2.50 eV, identified as A- and B-exciton, respectively [16].While, for other thicknesses, besides the A-, B-exciton, there exist two other reflection minima labeled as III and IV, respectively. By comparison, it can be seen that III and IV appeared in a certain thickness and energy red-shifted with the increase of thickness. Thus the thickness-dependent III and IV can be safely assigned to F-P cavity modes. But here we emphasize that III and IV are not bare cavity modes but hybrid cavity polaritons because of strong coupling between bare F-P cavity modes and excitons.

 

Fig. 2 Reflectance spectra for WS₂ flakes with d = 25 nm (black), d = 54 nm (red) and d = 70 nm (blue). R is raw data of sample, R_sub is white light source. The vertical red dashed lines label A- and B-exciton, respectively. The inset is a schematic of F-P cavity formed in the WS₂ flake.

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To clearly demonstrate the strong coupling of excitons-cavity modes in WS₂ flakes, a series of WS₂ flakes with thickness ranging from 49 nm to 76 nm were selected. Figure 3 presents the thickness-dependent reflectance spectra as a function of thickness. We can observe that both III and IV modes shifted gradually with thickness (guided by the red dashed lines). As the flakes became thinner, the IV mode blue-shifted and became closer to A exciton, while the III mode was gradually getting away from A exciton but approached to B exciton. As expected, it showed a typical anti-crossing behavior which manifested a strong coupling between cavity mode and excitons occurred. Obviously, in the WS₂ flakes, both A- and B-exciton participate in the formation of the cavity polaritons. Thus, three polariton branches: the lower polariton branch (LPB), middle polariton branch (MPB) and upper polariton branch (UPB) should be formed [35]. Here, III and IV modes can be assigned to LPB and MPB, respectively. The missing of UPB in spectra maybe due to the strong absorption originated from the strong electron (hole)-phonon coupling and the superposition of high-energy excited states of excitons [36–38 ].

 

Fig. 3 Thickness-dependent reflectance spectra of WS₂ flakes at various thickness ranging from 49 nm to 76 nm. The red dashed curves depict the cavity polaritons dispersion (LPB and MPB). The blue dashed lines indicate A- and B-exciton of WS₂.

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Furthermore, to better understand the cavity polaritons’ dispersions of WS₂ flakes, minima of each reflectance spectra were extracted by using multi-peak Lorentzian fitting and Coupled Oscillator Model, generally used for describing strong coupling of cavity modes-excitons [39], was adopted to fit the dispersion. Considering F-P cavity mode coupled with A- and B-exciton simultaneously, the eigen-states of cavity polaritons can be calculated by the Hamiltonian matrix:

 

Fig. 4 (a) The red squares with error bars are the cavity polariton dispersions extracted from the thickness-dependent reflectance spectra. The black solid lines are theoretically fitting calculated by coupled oscillator model for strong coupling. A- and B-exciton are labeled by dashed lines, and bare cavity mode (E_C) is shown as dot-dashed curve. (b) The fractions of each cavity polariton modes, in which, black triangles represent cavity photons, red forks represent A exciton and blue circles stand for B exciton.

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4. Conclusions

In conclusion, we have presented F-P cavity polaritons in WS₂ flakes by using home-made micro-reflectance equipment. The thickness-dependent reflectance spectra clearly showed a typical anti-crossing behavior and the formation of the cavity polaritons. By using the Coupled Oscillator Model for the strong coupling between excitons and cavity photons, the giant Rabi splitting were evaluated as ~270 meV for A exciton and ~780 meV for B exciton, respectively. Fractions of each polariton branch, obtained by calculating Hopfield mixing coefficients, gave a better understanding of cavity polaritons in TMDs. Our findings hold a great promise for the studies of exciton-based light-matter interaction in TMDs and their optical applications.