Correction of exciton binding energy in monolayer transition metal dichalcogenides

We theoretically investigate the corrections of exciton binding energy in monolayer transition metal dichalcogenides (TMDs) due to the exciton-optical phonon coupling in the Fr$\ddot{o}$hlich interaction model by using the linear operator combined Lee-Low-Pines variational method. We not only consider the excitons couple with the intrinsic longitudinal optical (LO) phonon modes, but also the surface optical phonon modes that induced by the polar substrates underneath the TMDs. We find that exciton binding energies are corrected in a large scale due to these exciton-optical phonon couplings. We discuss the dependences of exciton binding energy on the cut-off wave vector of optical phonon modes, the polarization parameters of materials and the interlayer distance between the polar substrates and TMDs. These results provide potential explanations for the divergence of the exciton binding energy between experiment and theory in TMDs.