  We investigate the correction of interlayer exciton binding energy in
transition metal dichalcogenides double layers arising from the exciton-optical
phonon coupling using the method of Lee-Low-Pines unitary transformation. We
find that the binding energy varies in several tens of meV, depending on the
polarizability of materials and interlayer distance between double layers.
Moreover, the correction of binding energy results in the remarkable increasing
of the critical temperature for the condensation of dilute excitonic gas basing
on the Berezinskii-Kosterlitz-Thouless model. These results not only enrich the
knowledge for the modulation of interlayer exciton, but also provide potential
insights for the Bose-Einstein condensation and superfluid transport of
interlayer exciton in two-dimensional heterostructures.
