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 $k^3$ 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.