| Electron ensemble in a superlattice in electric and magnetic fields displays plenty of physical phenomena due to the bounded electron motion in the Brillouin zone strengthened by electron chaotic behavior imposed by the applied magnetic field. We theoretically investigate transient and stationary drift currents of Bloch electrons in semiconductor superlattices subject 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 explained 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 phase loss of the oscillations is explored with a Monte Carlo method and compared with results of earlier models which use average-particle variables. It is found that average-particle-type models are not adequate to describe the resonance effects and lead to some artifacts like self-sustained oscillations or hysteresis effects, which do not exist in the Monte Carlo approach. The average particle description is an acceptable approximation only 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 to identify their relative importance. |
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