How can we know that the non-trivial band topology in a system is driven by spin-orbit coupling (SOC) or by band inversion?

Based on my understanding, SOC causes the band inversion and makes the system non-trivial, but I would like to make sure that my understanding is correct.

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    $\begingroup$ This answer may help: mattermodeling.stackexchange.com/questions/909/… $\endgroup$ – ProfM Jul 28 '20 at 10:23
  • $\begingroup$ @ProfM I'm just going through the unanswered queue right now, and came across this. This is not my area of expertise: does the user need to explain what is meant by "non-trivial band topology" ? or is that generally understood without further explanation? $\endgroup$ – Nike Dattani Jul 29 '20 at 16:17
  • $\begingroup$ @NikeDattani, thanks for this. I would say that it is probably understood -- it simply means a material that has non-zero topological invariants so cannot be adiabatically connected to the atomic limit. It is a term that is certainly used in talks/papers. $\endgroup$ – ProfM Jul 29 '20 at 17:11
  • $\begingroup$ @ProfM Thanks for the clarification. I had no idea what it would mean for a material to have trivial or non-trivial band topology. It seems like a simple enough question though: Do you know anyone that would know whether the non-trivial band topology is caused by band inversion or SOC or both? $\endgroup$ – Nike Dattani Jul 29 '20 at 17:15
  • $\begingroup$ @Alisufyan since this is one of the oldest unanswered questions now, can you tell us how you're doing with the question now? Was ProfM's comment helpful? Did you make progress on the question yourself? If so can you write an answer to help others in the future? If not is the answer still needed for you? I'm trying to clear up the unanswered queue! $\endgroup$ – Nike Dattani Dec 31 '20 at 4:43