Magnetic-field-enhanced transient and stationary drift currents of oscillating Bloch electrons in superlattices and limits of average-particle description in relation to Monte Carlo simulations

Abstract

We theoretically investigate transient and stationary drift currents of Bloch electrons in semiconductor superlattices subjected to an electric field along the growth axis and a magnetic field tilted with respect to the electric field. The magnetic-field-induced nonlinear coupling between the Bloch oscillations along the axis and in-plane cyclotron oscillations leads to a resonant phase-sensitive self-rectification of the oscillating currents. Both the transient motion of the particles after pulse excitation and the motion in the stationary state show this phenomenon. The effects have already been demonstrated experimentally but were discussed on the basis of different concepts. Here, we treat the transient and the stationary effect on equal footing using the model of the coupled oscillators. The relaxation and dephasing of the oscillations are explored with a Monte Carlo method and compared with results of models which use average-particle variables. It is found that average-particle-type models are not adequate to describe the resonance and relaxation effects of the ensemble satisfactorily. In the long-time limit and for strong coupling, they lead to some artifacts such as self-sustained oscillations or hysteresis effects, which do not exist in the Monte Carlo approach. The average-particle description is a qualitative approximation for weak coupling and if elastic scattering dominates. The shapes of the resonance curves in the Monte Carlo simulation sensitively depend on the details of the scattering mechanisms and allow us to identify their relative importance.