Nonlinear transport in two dimensions with Rashba–Dresselhaus spin–orbit coupling

Abstract

We report on a theoretical study on the nonlinear transport in two dimensions due to both Rashba (with strength α) and Dresselhaus (with strength β) spin–orbit couplings (SOCs). Based on the Boltzmann transport formalism, we study both the magnetic control of nonreciprocal charge transport and nonlinear Hall effect using a general Hamiltonian model. It is revealed that the nonlinear conductivity is significantly anisotropic and can be strongly modulated by the direction of a magnetic field as well as by SOC strengths. We further derive the analytic formulas in the weak-field or high-density regime, in good accordance with numerical results. Intriguingly, we demonstrate that the nonlinear conductivities satisfy the symmetry relations σxxx(2)(α,β)=−σyyy(2)(β,α) and σxyy(2)(α,β)=−σyxx(2)(β,α). Based on the magnetic control of nonlinear transport, we propose a simple electrical means to quantify the ratio α/β, which is quite useful to achieve the persistent spin texture in semiconductor quantum-well structures. Our work provides valuable insights into the nonlinear transport physics and open avenues to design anisotropic rectifying devices.