QUANTUM TRANSPORT IN SEMICONDUCTOR SUPERLATTICES BEYOND THE KADANOFF–BAYM ANSATZ

Abstract

Quantum transport in semiconductor superlattices subject to quantizing parallel electric and magnetic fields is studied based on the Kadanoff–Baym–Keldysh double-time Green function approach. Exploiting the symmetry properties of the underlying Hamiltonian, coupled kinetic equations are derived and analytically solved for the density-of-states and the carrier distribution function. Scattering giving rise to collisional broadening plays an important role in our transport model, whose unperturbed eigenstates are completely discrete due to Wannier–Stark and Landau quantization. It is shown that a correct description of the stationary quantum transport in superlattices with field-induced localized eigenstates requires the determination of a time-dependent distribution function from a kinetic equation, which emerges beyond the Kadanoff–Baym Ansatz. Depending on the scattering strength, gaps are predicted to occur in the electric and magnetic field dependence of the current density. The rigorous quantum-mechanical approach reveals the hopping nature of the nonlinear transport in narrow miniband superlattices. This is compared with results obtained recently within the density-matrix approach.