Coupled exciton internal and center-of-mass motions in two-dimensional semiconductors by a periodic electrostatic potential

We theoretically investigated the coupling between the exciton internal and center-of-mass motions in monolayer transition metal dichalcogenides subjected to a periodic electrostatic potential. The coupling leads to the emergence of multiple absorption peaks in the exciton spectrum which are the hybridizations of 1s, 2s and 2p$\pm$ Rydberg states with different center-of-mass momentums. The energies and wave functions of hybrid states can be strongly modulated by varying the profile of the periodic electrostatic potential, which well reproduces the recent experimental observations. Combined with the electron-hole exchange interaction, non-degenerate valley-coherent bright excitons can be realized by applying an in-plane electric field, with the valley coherence determined by the field direction.