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

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 σ_xxx⁽²⁾(α, β)=−σ_yyy⁽²⁾(β,α) and σ_xyy⁽²⁾(α,β)=−σ_yxx⁽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.