Specific features of the conductivity and spin susceptibility tensors of a two-dimensional electron gas with Rashba and Dresselhaus spin-orbit interactions

Abstract

The two-dimensional electron gas with spin-orbit interactions (SOIs) of Rashba and Dresselhaus types is known to form an anisotropic system with a Van Hove singularity in the density of states. Moreover, the ``amplitude'' and the energy position of this singularity depend on the ratio of the constants of Rashba $\ensuremath{\alpha}$ and Dresselhaus $\ensuremath{\beta}$ SOIs, $\ensuremath{\gamma}=\ensuremath{\beta}/\ensuremath{\alpha}$. Here the dependencies of the conductivity and spin susceptibility tensors on the position of the Fermi level are calculated for a wide range of $\ensuremath{\gamma}$. It is shown that if only the lower spin subband is filled the diagonal elements of the conductivity tensor have dips that appear when the Fermi level passes the singularity point both for $\ensuremath{\gamma}<1$ and $\ensuremath{\gamma}>1$. The amplitude of these features and their energy position depend on $\ensuremath{\gamma}$ and, in particular, for the state of persistent spin helix $\ensuremath{\gamma}=1$ they disappear. When only the lower spin subband is filled, the off-diagonal elements of the conductivity tensor are nonzero, that is, there is a Hall voltage due to the anisotropy of the Fermi surface and the scattering. In the region of filling of two spin subbands the ratio of diagonal and nondiagonal components of the spin susceptibility tensor is equal to $\ensuremath{\gamma}$ and in the conductivity tensor, the off-diagonal terms vanish.