Berry curvature induced spin currents in a 2D Rashba system

We study the linear and nonlinear spin currents in a two-dimensional (2D) gapped (induced by Zeeman splitting) Rashba spin-orbit coupled system using a modified spin current operator by including the anomalous velocity. The anomalous velocity of charge carriers induced by the Berry curvature gives rise to the linear spin Hall current, whereas the nonlinear spin current arises because of the band velocity and/or the anomalous velocity. We find that the linear spin current exhibits a plateau at the Zeeman gap, while the nonlinear spin currents shows peak at the gap edges. The magnitude of the peaks increases with the increasing strength of Zeeman gap. The linear spin current is always polarized out-of-plane, whereas the nonlinear spin currents have in-plane polarization. Further, we observe the generation of pure anomalous nonlinear spin current with spin polarization along the direction of propagation. These observations may provide useful hints to manipulate spin currents in Rashba systems.