Magnetotransport in a two-dimensional electron gas at large filling factors

Abstract

We derive the quantum Boltzmann equation for the two-dimensional electron gas in a magnetic field such that the filling factor $\ensuremath{\nu}\ensuremath{\gg}1.$ This equation describes all of the effects of the external fields on the impurity collision integral including Shubnikov--de Haas oscillations, the smooth part of the magnetoresistance, and nonlinear transport. Furthermore, we obtain quantitative results for the effect of the external microwave radiation on the linear and nonlinear dc transport in the system. Our findings are relevant for the description of the oscillating resistivity discovered by Zudov et al., the zero-resistance state discovered by Mani et al. and Zudov et al., and for the microscopic justification of the model of Andreev et al. We also present a semiclassical picture for the qualitative consideration of the effects of the applied field on the collision integral.