When we work on the topological insulator (protected by time reversal symmetry ), it is often said that the SOC is the main ingredient because it is a way to open a gap when the band inversion present. I want to ask what is the mechanism cause the gap to be opened ? More precisely, I found that SOC will cause the splitting of energy band. Let’s say if the system contain both time reversal and inversion symmetry, each energy band must be 2-fold degenerate. However the SOC term don’t violate these symmetries, where is the splitting come from ?
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$\begingroup$ I think figure 1 of this paper is kind of self-explanatory: arxiv.org/abs/1905.06508 $\endgroup$– Davide SangalliJul 7, 2022 at 21:19
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$\begingroup$ You can also have a look here: mattermodeling.stackexchange.com/a/1546/5685 $\endgroup$– Davide SangalliJul 8, 2022 at 18:38
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$\begingroup$ Were the comments by Davide helpful? Let us know if you're still working on this or if you found the answer! $\endgroup$– Nike DattaniFeb 6 at 18:41
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