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Velocity matrix element v[n,m] when band n and m are degenerate #8

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Echoxiangmega opened this issue May 10, 2023 · 1 comment
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@Echoxiangmega
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Dear Developers,

I am trying to calculate orbital Hall conductivity using HopTB, and I need to use the velocity matrix. But as shown in the code,
"v[n, m] is only correct when band m is nondegenerate or completely degenerate", so I wonder how to deal with the situation that band n and m are degenerate.
Thank you for your help

Best regards,
Pan

@atbug
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atbug commented May 15, 2023

The formalism of HopTB does not utilize degenerate perturbation theory. It is possible to extend current scheme to include degenerate bands, but right now the only way to do the calculation is to ignore degeneracies, since they occupy zero area in the Brillouin zone.

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