Sign Changes of Intrinsic Spin Hall Effect in Semiconductors and Simple Metals: First-Principles Calculations

First-principles calculations are applied to study spin Hall effect in semiconductors and simple metals. We found that intrinsic spin Hall conductivity (ISHC) in realistic materials shows rich sign changes, which may be used to distinguish the effect from the extrinsic one. The calculated ISHC in $n$-doped GaAs can be well compared with experiment, and it differs from the sign obtained from the extrinsic effect. On the other hand, the ISHC in W and Au, which shows opposite sign, respectively, is robust and not sensitive to the disorder.

Figure 1

The calculated (a) band structure, (b) spin Hall conductivity ${\sigma }_{xy}$ as function of Fermi level position for bulk GaAs. We define the converged Fermi level without doping as energy zero point, and evaluate ${\sigma }_{xy}$ by rigidly shifting the Fermi level position. The panel (c) gives the ${\sigma }_{xy}$ of $n$-GaAs as functions of carrier (electron) density after subtracting the part that does not contribute to spin accumulation (see the text part for explanation). Note the factor of 10 for the $T=30\mathrm{K}$ and $\delta =16\mathrm{meV}$ curve.

Figure 2

The calculated (a) band structure, (b) spin Hall conductivity ${\sigma }_{xy}$ as function of Fermi level position for bulk Si.

Figure 3

The same notation as shown in Fig. 2, but for W.

Figure 4

The same notation as shown in Fig. 2, but for Au.