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Chern number calculation by discretized brillouin zone method as discussed in Fukui paper, anybody can give example where this detail analysis of this method has been used?

The paper is Takahiro Fukui, Yasuhiro Hatsugai, Hiroshi Suzuki, "Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances".

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This method was used in a paper by Essen and Moore 1 that was published in PRB in 2007.

Please note, this is very slow by today's standards.

As to numerical methods that give a Z2 index in 2D, here are some more recent papers.

[2] Huang, Huaqing, and Feng Liu. "Quantum spin Hall effect and spin Bott index in a quasicrystal lattice." Physical review letters 121.12 (2018): 126401.

[3] Loring, Terry A., and Matthew B. Hastings. "Disordered topological insulators via C*-algebras." EPL (Europhysics Letters) 92.6 (2011): 67004.

[4] Li, Zhi, and Roger SK Mong. "Local formula for the Z 2 invariant of topological insulators." Physical Review B 100.20 (2019): 205101.

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  • $\begingroup$ Would you be willing to point us to some references with more efficient methods? $\endgroup$
    – d_b
    Jul 29, 2021 at 18:34
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    $\begingroup$ I added a few. There are lots of papers that mention the spin Bott number. $\endgroup$
    – Terry Loring
    Jul 29, 2021 at 19:25
  • $\begingroup$ Thanks. Can you share any python code for any 3 band system using Fukui paper method? $\endgroup$
    – Physik
    Aug 24, 2021 at 19:49
  • $\begingroup$ I have not implemented this method. $\endgroup$
    – Terry Loring
    Aug 24, 2021 at 21:22

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