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30: Gallium Arsenide — Frequency-dependent spin Hall conductivity

  • Outline: Calculate the alternating current (ac) spin Hall conductivity of gallium arsenide considering spin-orbit coupling. To gain a better understanding of this example, it is suggested to read Ref. 1 for a detailed description of the theory and Ch. 12.5 of the User Guide.

  • 1-6: Compute the MLWFs and compute the ac spin Hall conductivity.

ac spin Hall conductivity

The ac SHC of GaAs converges rather slowly with \(k\)-point sampling, and a \(100 \times 100 \times 100\) kmesh does not yield a well-converged value. To get a converged SHC value, increase the density of kmesh and then compare the converged result with those obtained in Refs. 1.

The file GaAs-shc-freqscan.dat contains the calculated ac SHC. The snippet below shows a calculated result with \(100\times100\times100\) kmesh, a fixed smearing width of 0.05 eV and no scissors shift applied.

100×100×100 kmesh
#No.   Frequency(eV)   Re(sigma)((hbar/e)*S/cm)   Im(sigma)((hbar/e)*S/cm)
   1     0.000000    -0.68114601E+00    0.00000000E+00
...
 801     8.000000    -0.39471936E+01   -0.29928198E+02

The ac SHC is plotted as Figure 1.

Image title
Frequency scan plot for GaAs ac SHC, using a low kmesh of \(100\times100\times100\).

If further increasing the density of kmesh to \(250\times250\times250\), and using the adaptive smearing, a nice converged plot could be produced as Figure 2. Note that by using keywords

Input file
shc_bandshift = true
shc_bandshift_firstband = 9
shc_bandshift_energyshift = 1.117

a scissors shift of 1.117 eV is applied. Figure 2 can be viewed as Figure 1 translated by \(\sim1\) eV along the horizontal axis.

Image title
Frequency scan plots for GaAs ac SHC, using a dense kmesh of \(250\times250\times250\). Two kinds of smearing are compared.

  1. Junfeng Qiao, Jiaqi Zhou, Zhe Yuan, and Weisheng Zhao. Calculation of intrinsic spin hall conductivity by wannier interpolation. Phys. Rev. B, 98:214402, Dec 2018. URL: https://link.aps.org/doi/10.1103/PhysRevB.98.214402, doi:10.1103/PhysRevB.98.214402. ↩↩