Self-dressing dynamics of slow electrons in covalent crystals

Abstract

We consider a slow monoelectronic excitation in a covalent crystal at T=0. The interaction with the zero-point longitudinal acoustic phonons leads to the formation of a dressed state, made by the electron accompanied by a deformation field, which has energy lower than the corresponding bare monoelectronic state. To describe the dynamics of the self-dressing process we study the time development of the permanence probability amplitude, Ae(t), in the initial bare monoelectronic state. To follow its time development for long enough times it is necessary to use nonperturbative techniques. In order to be able to follow the decrease of the electron’s energy we use a modified van Hove resolvent theory. We show that Ae(t) decays exponentially with a meanlife time τe long compared with the inverse Debye frequency ωD−1.