Separation of the valley exciton-polariton in two-dimensional semiconductors with an anisotropic photonic crystal

Excitons in two-dimensional (2D) transition metal dichalcogenides (TMDC) are stable at room temperature because of high exciton binding energies. They can be selectively addressed based on the unique optical selection rules from angular momentum conservation for the $K/{K}^{\ensuremath{'}}$ valley state and the helicity of circularly polarized light. When coupled with the optical modes in optical cavities, excitons can form exciton-polaritons, exploiting which in 2D TMDC may lead to optoelectronic devices for room temperature operation. The valley degree of freedom of the excitons, however, is mostly lost when forming exciton-polaritons because the cavity mode usually does not have a well-defined spin angular momentum. Here, we theoretically demonstrate that the valley information of exciton-polaritons can be preserved and resolved in a photonic cavity made of birefringent materials. Because of the optical anisotropy, the guided resonance modes have a net transverse spin angular momentum and selectively couple to exciton-polaritons with the corresponding valley state. In the strong-coupling regime, the exciton-polariton behaves in a way like the Rashba effect in the solid. The dispersion of the $K/{K}^{\ensuremath{'}}$ exciton-polariton splits in momentum space based on its valley state, similar to electron spins in Rashba systems. Realizing valley-dependent exciton-polaritons affords a possibility to explore valley exciton dynamics in a strongly coupled system and will contribute to the study of excitonic, polaritonic devices, Bose-Einstein condensation, and superfluidity in semiconductors.