Identification of a state of persistent spin helix in a parallel magnetic field, and exploration of its transport properties

Abstract

The tensors of conductivity and spin susceptibility of a two-dimensional electron gas (2DEG) with equal Rashba and Dresselhaus spin-orbit interaction constants [the persistent spin helix (PSH) state] in a parallel magnetic field are calculated. Applying a parallel magnetic field to the PSH state leads to the appearance of a saddle point in the spectrum and, accordingly, to a Van Hove singularity (VHS), whose amplitude increases indefinitely as the magnetic field strength $(\mathbf{b})$ approaches to some critical value ${b}_{cr}$. The presence of a VHS in the density of states is an important factor determining the conductivity and spin susceptibility tensors. When only the lower spin subband is filled, the off-diagonal elements of the conductivity tensor are nonzero; that is, a Hall voltage arises due to the anisotropy of the Fermi surface and scattering. In the region where two spin subbands are filled, the diagonal and off-diagonal components of the spin susceptibility tensor are equal, and the off-diagonal terms of the conductivity tensor vanish. A sharp decrease in the conductivity and spin susceptibility at the beginning of the filling of the second spin subband, the ratio of the diagonal component of the spin susceptibility to the off-diagonal one, and also the number of critical points in the spectrum make it possible to establish the PSH 2DEG state.