30: Gallium Arsenide Frequency-dependent spin Hall conductivity¶
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Outline: Calculate the alternating current (ac) spin Hall conductivity of gallium arsenide considering spin-orbit coupling. To gain a better understanding of this tutorial, it is suggested to read Ref. 1 for a detailed description of the theory and the berry_task=shc: spin Hall conductivity chapter of the User Guide.
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Directory:
tutorials/tutorial30/
Files can downloaded from here -
Input files
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GaAs.scf
Thepwscf
input file for ground state calculation -
GaAs.nscf
Thepwscf
input file to obtain Bloch states on a uniform grid -
GaAs.pw2wan
The input file forpw2wannier90
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GaAs.win
Thewannier90
andpostw90
input file
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Run
pwscf
to obtain the ground state of gallium arsenide -
Run
pwscf
to obtain the Bloch states on a uniform \(k\)-point grid -
Run
wannier90
to generate a list of the required overlaps (written into theGaAs.nnkp
file) -
Run
pw2wannier90
to compute the overlaps between Bloch states and the projections for the starting guess (written in theGaAs.mmn
andGaAs.amn
files) -
Run
wannier90
to compute the MLWFs -
Run
postw90
- serial execution
- example of parallel execution with 8 MPI processes
ac spin Hall conductivity¶
The spin Hall conductivity is also dependent on the frequency \(\omega\) in this equation of the User Guide. The direct current (dc) SHC calculated in the previous tutorial corresponds to \(\sigma_{\alpha\beta}^{\text{spin}\gamma}\) in the limit \(\omega\rightarrow 0\) and it is a real number. At finite frequency \(\sigma_{\alpha\beta}^{\text{spin}\gamma}\) acquires an imaginary part.
To compute the ac spin Hall conductivity for \(\hbar\omega\) up to 8 eV, add the lines
and re-run postw90
. The file GaAs-shc-freqscan.dat
contains the
calculated ac SHC. Reasonably converged spectra can be obtained with a
\(250\times 250\times 250\) \(k\)-point mesh. To plot the ac SHC, issue the
following commands
plot 'GaAs-shc-freqscan.dat' u 2:3 w l title 'Re',
'GaAs-shc-freqscan.dat' u 2:4 w l title 'Im'
and then compare the result with Fig. 4 in Ref. 1 or the Solution Booklet.
Notes¶
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When calculating ac SHC, adaptive smearing can be used by add the following keywords in the
GaAs.win
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Adaptive kmesh refinement is not implemented for ac SHC calculation.
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The first 10 semi-core states are excluded from the calculation by using the following keywords
and in the case of GaAs disentanglement is not adopted so
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Since the band gap is often under estimated by LDA/GGA calculations, a scissors shift is applied to recover the experimental band gap by using the following keywords
or by
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Junfeng Qiao, Jiaqi Zhou, Zhe Yuan, and Weisheng Zhao. Calculation of intrinsic spin hall conduc tivity by wannier interpolation. Phys. Rev. B, 98:214402, Dec 2018. URL: https://link.aps.org/doi/10.1103/PhysRevB.9 8.214402, doi:10.1103/PhysRevB.98.214402. ↩↩