Acoustical polaron in three dimensions: The ground-state energy and the self-trapping transition.

Abstract

The interaction of an electron with acoustical phonons by the deformation potential is studied with the Feynman path-integral method for zero temperature. An upper bound to the polaron ground-state energy is obtained. The nature of the transition of the quasifree to the self-trapped electron state is discussed for different approximations to the polaron ground-state energy. We find that, within the Feynman approximation, which is the most reliable one for the ground-state energy, there exists a critical value (${k}_{0}^{\mathrm{*}}$) for the cutoff (${k}_{0}$) in phonon wave-vector space such that for ${k}_{0}$${k}_{0}^{\mathrm{*}}$ (${k}_{0}$>${k}_{0}^{\mathrm{*}}$) the self-trapping transition is continuous (discontinuous) as a function of the electron-phonon coupling strength.