Diffusive magnetotransport in a two-dimensional electron gas in the presence of Rashba spin-orbit interaction

Abstract

An analytical approach to calculation of the conductivity tensor $\ensuremath{\sigma}$ of a two-dimensional electron system with Rashba spin-orbit interaction (SOI) in an orthogonal magnetic field is proposed. The electron momentum relaxation is assumed to be due to electron scattering by a random field of short-range impurities, which is taken into account in the Born approximation. An exact expression for the one-particle Green's function of an electron with Rasba SOI in an arbitrary magnetic field is suggested. This expression allows us to obtain analytical formulas for the density of states and $\ensuremath{\sigma}$ in the self-consistent Born and ladder approximations, respectively, which hold true in a wide range of magnetic fields, from the weak $({\ensuremath{\omega}}_{c}\ensuremath{\tau}\ensuremath{\ll}1)$ up to the quantizing $({\ensuremath{\omega}}_{c}\ensuremath{\tau}\ensuremath{\gtrsim}1)$ ones. It is shown that in the ladder approximation the Rashba SOI has no effect at all on the conductivity magnitude in the whole range of classical (nonquantizing) magnetic fields. The Shubnikov--de Haas oscillation period is shown to be related to the total charge carrier concentration by the conventional formula, irrespective of the SOI magnitude. A simple equation defining the location of the SdH oscillation beating nodes is obtained. The results are in good agreement with the experimental and recent numerical investigations.