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

Abstract

The problem of the nonlinear spin-currents generated by an electric field $\mathbf{E}$ and a temperature gradient $\mathbf{\ensuremath{\nabla}}T$ in spin-orbit coupled systems is revisited in a different formalism. Here, the second-order correction to the particle distribution function $\ensuremath{\delta}{f}^{(2)}$ 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 $\ensuremath{\delta}{f}^{(2)}$ 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 $\ensuremath{\alpha}$ and Dresselhaus $\ensuremath{\beta}$ interactions. For the whole range of $\ensuremath{\alpha}$ versus $\ensuremath{\beta}$ values, we obtain analytic results for all the spin currents that can be driven in the system, proportional with ${\mathbf{E}}^{2}$, $\mathbf{\ensuremath{\nabla}}{T}^{2}$, or with $\mathbf{E}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{\ensuremath{\nabla}}T$. The magnitude of these currents is smaller than previously anticipated.