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

HopTB / HopTB.jl

Tight-binding package written in Julia

MIT License

53 stars 7 forks source link

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

Open Echoxiangmega opened 1 year ago

Echoxiangmega commented 1 year ago

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 commented 1 year ago

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.