Probing Excitonic Rydberg States by Plasmon Enhanced Nonlinear Optical Spectroscopy in Monolayer WS₂at Room Temperature

The optoelectronic properties of two-dimensional (2D) transition metal dichalcogenide (TMDC) monolayers such as WS₂are largely dominated by excitons due to strong Coulomb interactions in these 2D confined monolayers, which lead to formation of Rydberg-like excitonic states below the free quasiparticle band gap. The precise knowledge of high order Rydberg excitonic states is of great importance for both fundamental understanding such as many-electron effects and device applications such as optical switching and quantum process information. Bright excitonic states could be probed by linear optical spectroscopy, while probing dark excitonic states generally requires nonlinear optical (NLO) spectroscopy. Conventional optical methods for probing high-order Rydberg excitonic states were generally performed at cryogenic temperatures to ensure enough signal-to-noise ratio (SNR) and narrow line width. Here we have designed a hybrid nanostructure of monolayer WS₂integrated with a plasmonic cavity and investigated their NLO properties at the single particle level. Giant enhancement in NLO responses, stronger excitonic resonance effects, and narrowed line widths of NLO excitation spectra were observed when monolayer WS₂was placed in our carefully designed plasmonic cavity. Optimum enhancement of 1000-, 3000-, and 3800-fold were achieved for two-photon photoluminescence (2PPL), second harmonic generation (SHG), and third-harmonic generation (THG), respectively, in the optimized cavity structure. The line width of SHG excitation spectra was reduced from 43 down to 15 meV. Plasmon enhanced NLO responses brought improved SNR and spectral resolution, which allowed us to distinguish discrete excitonic states with small energy differences at room temperature. By using three complementary NLO techniques in combination with linear optical spectroscopy, energies of Rydberg excitonic states of A (1s, 2s, 2p, 3s, 3p, 4s), B (1s), and C and D excitons of monolayer WS₂have been accurately determined, which allow us to determine exciton binding energy and quasiparticle bandgap. It was interesting to find that the 2p lies 30 meV below 2s, which lends strong support to the theoretical prediction of nonlocal dielectric screening effects based on a non-hydrogenic model. Our results show that plasmon enhanced NLO spectroscopy could serve as a general method for probing high order Rydberg excitonic states of 2D materials.