Discontinuity in the Polaron Ground State

Abstract

With Feynman's path integral method applied to an electron interacting with acoustic as well as with optical modes of lattice vibrations, it is shown that the abrupt change, as coupling increases, of the polaron state from nearly free type to self-trapping type is caused by the short range interaction (deformation potential due to acoustic vibrations) but not by the long range interaction (electric polarization field due to optical vibrations), in agreement with previous argument. Whether or not one takes into account the discreteness of electron coordinate has no relevance to the very existence of the abrupt change, although the quasi-continuum model leads to underestimation of its magnitude. When the rigid lattice band width is not large compared to the average phonon energy, however, one can no more distinguish between the nearly free state and the self-trapping state in a clear-cut way.