Spin-Hall transport of heavy holes in III-V semiconductor quantum wells

We investigate spin transport of heavy holes in III-V semiconductor quantum wells in the presence of spin-orbit coupling of the Rashba type due to structure-inversion asymmetry. Similarly to the case of electrons, the longitudinal spin conductivity vanishes, whereas the off-diagonal elements of the spin-conductivity tensor are finite giving rise to an intrinsic spin-Hall effect. For a clean system we find a closed expression for the spin-Hall conductivity depending on the length scale of the Rashba coupling and the hole density. In this limit the spin-Hall conductivity is enhanced compared to its value for electron systems, and it vanishes with increasing strength of the impurity scattering. As an aside, we also derive explicit expressions for the Fermi momenta and the densities of holes in the different dispersion branches as a function of the spin-orbit coupling parameter and the total hole density. These results are of relevance for the interpretation of possible Shubnikov–de Haas measurements detecting the Rashba spin splitting.

Figure 1

The Fermi wave numbers $k_f^{\pm }$ and the difference $\Delta n$ of hole densities in the two dispersion branches as a function of the characteristic length $m\alpha ∕{\hslash }^2$ of the Rashba coupling at a total hole density of $n=3\times {10}^{14}{\mathrm{m}}^{-2}$.

Figure 2

The spin-Hall condcutivity for dominating Rashba coupling [${\epsilon }_R⪢\hslash ∕\tau$, see Eq. (27)] as a function of $m\alpha ∕{\hslash }^2$ at a total hole density of $n=3\times {10}^{14}{\mathrm{m}}^{-2}$.