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

TL;DR

This work shows that in time-reversal-symmetric 2D spin-orbit–coupled systems, the in-plane spin current vanishes at linear order and a non-linear (second-order) in-plane spin current arises from the spin Berry curvature polarizability (SBCP). Using a Boltzmann-relaxation framework, the authors derive expressions for SBC and SBCP and apply them to a 2D heavy-hole gas with $k^3$ Rashba–Dresselhaus SOC, revealing both transverse and longitudinal second-order spin currents, with anisotropy enabling collinearly polarized currents. They further explore radiation-induced anisotropy via Floquet-Magnus theory, showing giant non-linear spin responses near degeneracies and highlighting substantial intrinsic contributions with radiation-driven enhancement of extrinsic effects. The findings provide a mechanism to control in-plane spin currents in spintronic devices through SOC anisotropy or external radiation, offering tunable, low-dissipation spin transport channels with potential practical impact.

Abstract

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.

Figures (8)

• Figure 1: Two spin-split energy bands versus $\tilde{k}_x$ for $\beta/\alpha = 0.5$ are shown. Here $k_F^{\pm}$ are for a given Fermi energy.
• Figure 2: Linear spin Hall conductivity of the hole gas versus the scaled Fermi energy ($\varepsilon/\varepsilon_h$) for different values of $\beta/\alpha$.
• Figure 3: Density plots of the in-plane SBCP components for the $\varepsilon_+({\bf k})$ band in the $k_x$-$k_y$ plane: (a) pure Rashba case ($\beta =0$); (b) Rashba-Dresselhaus case ($\beta/\alpha =0.4$).
• Figure 4: Second-order spin conductivity vs. Fermi energy (in units of $\varepsilon_h$). Top panel: variation of intrinsic second-order spin conductivity with Fermi energy for (a) $\beta/\alpha=0$ (b) $\beta/\alpha=0.4$. The scale of $\Gamma^{l,\text{int}}_i$ is set at $\Gamma_0\times10^6$, with $\Gamma_0 = e^2\tilde{S}_0/(16\alpha k_h^4)$. Bottom panel: extrinsic contribution to second-order spin conductivity (in units of $\Gamma_0$) for (c) $\beta/\alpha=0$ (d) $\beta/\alpha=0.4$. The relaxation time $\tau$ is chosen to be $1\:\rm{ps}$.
• Figure 5: Dispersion of Rashba spin-orbit coupled hole gas in the presence of electromagnetic radiation for $\phi=\pi/4$, $A= 0.15$ and $\alpha_0=0.04$. The band degeneracy occurs at $\tilde{k}=0.387$ and the corresponding energy is about 0.075 in the given scale.