Quantum theory of high-electric-field magnetotransport for a two-dimensional electron gas in microstructures

Abstract

Nonlinear response to an electric field applied in the plane of a two-dimensional electron gas (2DEG) subjected to a perpendicular magnetic field is expressed in terms of an electric-field (F)-dependent magnetoconductivity in which the effect of the electric field is incorporated in the resolvent of the Liouville operator. This electric-field-dependent Kubo-type formula is calculated in the presence of the simultaneous scattering by disorder and phonons and is expressed in terms of the electric-field-dependent broadening and shifting of the Landau levels. It is found to be essential to treat the two interactions simultaneously and self-consistently at low temperatures. High-field effects such as «collisional broadening» and «intracollisional field effects» as manifested through the electric-field-dependent tetradic self-energy of 2DEG in a perpendicular magnetic field are calculated and shown to be much more pronounced in 2DEG as compared to the same phenomenon in three-dimensional semiconductors. The present results are found to be useful in the calculation of the effects of the temperature (T), magnetic field (B) and the electric field (F) as well as the interplay of the two interactions on the quantum effects as manifested in the Landau level broadening due to the relaxation and acceleration of the electrons in an applied electric field. In the limitF→0 the present results reduce to the usual formulae as known from the linear response theory.