Spin Hall and longitudinal conductivity of a conserved spin current in two dimensional heavy-hole gases

TL;DR

This paper investigates the spin Hall and longitudinal conductivities in 2D heavy-hole gases with k-cubic Rashba and Dresselhaus interactions, highlighting the impact of a conserved spin current definition on measurable spin transport properties.

Contribution

It introduces a new definition of spin current for spin-3/2 holes and analyzes its effects on spin conductivity in 2D heavy-hole gases, revealing distinct anisotropic responses.

Findings

Spin Hall conductivity varies significantly with the type of spin-orbit coupling.

The alternative spin current definition affects the magnitude and sign of the spin current.

Non-zero spin Hall conductivity occurs when Rashba and Dresselhaus couplings are equal.

Abstract

The spin Hall and longitudinal conductivity of a 2D heavy-hole gas with {\it k}-cubic Rashba and Dresselhaus spin-orbit interaction is studied in the ac frequency domain. Using Kubo linear-response theory and a recently proposed definition for the (conserved) spin current operator suitable for spin-3/2 holes, it is shown that the spin conductivity tensor exhibit very distinguishable features from those obtained with the standard definition of the spin current. This is due to a significant contribution of the spin-torque term arisen from the alternative definition of spin current which strongly affects the magnitude and the sign of the dynamic spin current. In the dc (free of disorder) limit, the spin Hall conductivity for only (or dominant) {\it k}-cubic Rashba coupling is $\sigma^{s,z}_{xy}(0)=-9e/8\pi$, whereas $\sigma^{s,z}_{xy}(0)=-3e/8\pi$ for only (or dominant) {\it k}-cubic Dresselhaus coupling. Such anisotropic response is understood in terms of the absence of mapping the {\it k}-cubic Rashba $\leftrightarrow$ Dresselhaus Hamiltonians. This asymmetry is also responsible for the non-vanishing dc spin Hall conductivity ($\sigma^{s,z}_{xy}(0)=-6e/8\pi$) when the Rashba and Dresselhaus parameters have the same strength, in contrast with its corresponding case for electrons. These results are of relevance to validate the alternative definition of spin-current through measurements in the frequency domain of the spin accumulation and/or spin currents in 2D hole gases.