Nonlinear spin-current generation in quantum wells with arbitrary Rashba-Dresselhaus spin-orbit interactions

The problem of the nonlinear spin-currents generated by an electric field E and a temperature gradient ∇T in spin-orbit coupled systems is revisited in a different formalism. Here, the second-order correction to the particle distribution function δf⁽²⁾ is derived in a semiclassical approximation that takes into account the local change in the equilibrium distribution function induced by the external fields. Our approach departs significantly from the present theory, where δf⁽²⁾ is written as an iterative solution to the Boltzmann transport equation in the relaxation-time approximation. As we show, such an expression does not actually satisfy the collision term of the equation, and therefore it is not self-consistent. We apply our formalism to the case of a quantum well with arbitrary values of the linear Rashba α and Dresselhaus β interactions. For the whole range of α versus β values, we obtain analytic results for all the spin currents that can be driven in the system, proportional with E², ∇T², or with E·∇T. The magnitude of these currents is smaller than previously anticipated.