[Wannier] gauge problems in mmn file

[chong wang]

Dear wannier users and developers:

I have been working on velocity matrix(berry connection of different bands) in band theory recently. Since wannier code does not output velocity matrix, I have been looking at the source code these days.

As you have probably known, calculating of berry connection suffers 'smooth gauge problem’. That is, since bloch wave functions can be multiplied by an arbitrary phase, one must obtain a smooth gauge for bloch wave functions to calculate finite difference.

I noticed that some source code directly used discrete versions of formula in MV90(Maximally localized generalized Wannier functions for composite energy bands), which requires ‘mmn' matrix to be continuous in brillouin zone. Initial ‘mmn’ matrix is read from .mmn file. Does this mean in .mmn file gauge has already been fixed in some way?

Looking forward to your reply!

Best！

Chong Wang