Role of Berry curvature in the generation of spin currents in Rashba systems
Priyadarshini Kapri, Bashab Dey, Tarun Kanti Ghosh
Abstract
We study the background (equilibrium), linear, and nonlinear spin currents in two-dimensional (2D) Rashba spin-orbit coupled systems with Zeeman splitting and in three-dimensional (3D) noncentrosymmetric metals using a modified spin current operator by inclusion of the anomalous velocity. The linear spin Hall current arises due to the anomalous velocity of charge carriers induced by the Berry curvature. The nonlinear spin current occurs due to the band velocity and/or the anomalous velocity. For 2D Rashba systems, the background spin current saturates at high Fermi energy (independent of the Zeeman coupling), linear spin current exhibits a plateau at the ``Zeeman'' gap, and nonlinear spin currents are peaked at the gap edges. The magnitude of the nonlinear spin current peaks enhances with the strength of Zeeman interaction. The linear spin current is polarized out-of-plane, while the nonlinear ones are polarized in-plane. We witness pure anomalous nonlinear spin current with spin polarization along the direction of propagation. In 3D noncentrosymmetric metals, background and linear spin currents are monotonically increasing functions of Fermi energy, while nonlinear spin currents vary nonmonotonically as a function of Fermi energy and are independent of the Berry curvature. These findings may provide useful information to manipulate spin currents in Rashba spin-orbit coupled systems.