  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.
