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Recent studies classified "intrinsic", "symmetry protected", and other topological properties of matter. The paper (Topological states in photonic systems) claims that "The transport of many topological interfacial states is immune to fabrication imperfections".

This is a really strong statement. When are topological edge/interface states immune to what disorder? I'm reminded of the IQHE experiment, showing that disorder affects the plateaus of hall conductance.And if disorder is large enough, it may change the value of hall conductance.(Reference?)

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  • $\begingroup$ Great! It's certainly something nowhere near my expertise/familiarity, but it sounds like a pretty solid question, so hopefully you'll find a few people who know enough about it to offer thoughts :-) $\endgroup$ Feb 24, 2017 at 7:38
  • $\begingroup$ Usually, symmetry protected states remains stable unless the symmetry is explicitly broken, or the gap closes for some reason or another. In particular, one has to be vigilant with respect to time-dependent interactions, since those ones may easily generate excitations above the gap. In that case, the problem becomes model dependent (as far as I know). A good symmetry for protection is time-reversal invariance (TRI), since it is relatively easy to experimentally protect against magnetic effect (the main cause of breaking the TRI). This is the reason why superconducting state is stable. $\endgroup$
    – FraSchelle
    Feb 25, 2017 at 9:17
  • $\begingroup$ Hi, FraSchelle, superconducting state is not necessarily topological, could provide some reference related? $\endgroup$
    – Wilson Ko
    Feb 27, 2017 at 12:09
  • $\begingroup$ @WilsonKo Please use @ Fraschelle (without space) to let me noticed of your comment. References about symmetry protected topological order in superconductor are arxiv.org/abs/cond-mat/0404327 and arxiv.org/abs/1105.5031 $\endgroup$
    – FraSchelle
    May 7, 2017 at 8:31

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