I want to calculate the band parity at some TRIM (time-reversal invariant momentum) point in Brillouin zone. Parity was defined as the eigenvalue of the inversion operator. My question is how to construct the matrix representation of the parity operator to calculate the band parity at a TRIM point given a crystal and the tight binding matrix?

  • $\begingroup$ +1. I tried to edit this to make it more clear, but if you feel any part would be better left as it was before, then please feel free to change things back! Hopefully you get an answer soon! $\endgroup$ Jul 7, 2021 at 19:03
  • $\begingroup$ So given a tight binding matrix for a crystal, you want the matrix representation of the operator that calculates the band parity at a TRIM point, where parity means "eigenvalue of the inversion operator"? $\endgroup$ Dec 25, 2021 at 20:59
  • $\begingroup$ I'm a little confused by the distinction between "parity" and "inversion". If you are defining parity to be the eigenvalue(?) of the inversion operator, then wouldn't that be the operator you are looking for? Its not clear to me how you would define an operator for a single eigenvalue. $\endgroup$
    – Tyberius
    Dec 30, 2021 at 16:41
  • $\begingroup$ This question appears to be abandoned. It can be reopened if OP addresses questions/suggestions in the comments or anyone else wants to provide an answer. $\endgroup$
    – Tyberius
    Jan 13, 2022 at 2:10