Quantum transport and solid-state dynamics for Bloch electrons in an electric field

Abstract

A novel formalism for treating Bloch electron dynamics and quantum transport in electric fields of arbitrary strength and time dependence is presented. In this formalism, the electric field is described through the use of the vector potential; this choice of gauge leads to a natural set of basis functions for describing Bloch electron dynamics in an electric field, even if the field is inhomogeneous . Quantum transport results for Bloch electrons in a spatial homogeneous but arbitrarily time dependent electric field undergoing elastic scattering from randomly distributed impurities (Kohn-Luttinger revisited) are presented; that is, a non-linear “Boltzmann equation” is derived with collision integrals involving not only memory and intracollisional field effects, but also including explicit band-mixing transients such as effective mass dressing and Zener tunneling. The application of this formalism to quantum transport in inhomogeneous electric fields is also addressed; specific applications to problems involving tunneling through “band-engineered” tunneling barriers and impurity scattering in electric fields of arbitrary strength and time dependence are discussed.