Quantum transport for Bloch electrons in inhomogeneous electric fields

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Abstract
A novel formalism for treating Bloch-electron dynamics and quantum transport in inhomogeneous 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 addition, a basis set of localized, electric-field-dependent Wannier functions is established and utilized to derive a quantum ‘‘Boltzmann equation’’ which includes explicit band-mixing transients such as effective-mass dressing and Zener tunneling. The application of this formalism to quantum transport in spatially localized inhomogeneous electric fields which occur in problems involving tunneling through ‘‘band-engineered’’ tunneling barriers and impurity scattering is discussed.