Quantum transport for electron quasiparticles interacting with a disordered binary alloy: A Wigner approach

Abstract

Quantum transport is developed in the Wigner function representation for a Bloch electron quasiparticle interacting with a disordered binary alloy in the presence of a homogeneous electric field of arbitrary time dependence and amplitude. The electron quasiparticle is described by a single-band effective Hamiltonian, and the homogeneous electric field is treated in the vector potential gauge. The methodology for the quantum transport analysis proceeds by first transforming the Liouville equation to one in which the interaction Hamiltonian (the binary alloy Hamiltonian) appears quadratically. The basis states employed in evaluating the requisite matrix elements are the instantaneous eigenstates of the electron quasiparticle Hamiltonian in the presence of the electric field. The Wigner quantum transport equations are derived, and the binary alloy collision term is suitably ensemble averaged over the disordered binary alloy matrix elements. In addition, the general drift and diffusion terms are exactly obtained, resulting in the complete Wigner-Boltzmann equation for the binary alloy system. In approximating the collision term for the two separate cases of parabolic energy dispersion and the long-wavelength limit, it is found that the reduced Wigner-Boltzmann equation includes the manifestation of the intracollisional field effect and other quantum generalities. As a contrast to the actual random alloy treatment, attention is given to the canonical problem of quantum transport for a virtual crystal (VC). As an alternative to the random binary alloy scattering problem, the VC Hamiltonian adopted for this treatment is derived by ensemble averaging the random binary alloy Hamiltonian. The resulting Wigner transport equation for the VC case is descriptive of Bloch dynamics in a graded semiconductor alloy.