Non-linear in-plane spin current in spin–orbit coupled 2D hole gases

The non-linear transport of charge and spin due to the emergence of band geometric effects has garnered much interest in recent years. In this work, we show that a linear in-plane spin current vanishes, whereas a non-linear (second-order) in-plane spin current exists for a generic two-dimensional system having time-reversal symmetry. The intrinsic second-order spin current originates from the spin Berry curvature polarizability. The formulation when applied to 2D hole gases with the k3 Rashba spin–orbit coupling reveals the existence of both transverse and longitudinal second-order spin currents normal to the spin orientation. Interestingly, anisotropic spin–orbit couplings can generate collinearly polarized spin current (spins polarized in the direction of spin current) in the second-order. The effects of anisotropy are explored by introducing an additional Dresselhaus spin–orbit coupling and electromagnetic radiation over the isotropic Rashba system. The generation and control over the multiple in-plane spin currents may have important applications in spintronic devices.