# Under what conditions are topological edge/interface states immune to random disorder?

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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?)

This post imported from StackExchange Physics at 2017-03-05 22:13 (UTC), posted by SE-user Wilson Ko
retagged Mar 5, 2017
Hi Wilson, I further edited your question to try to ensure it makes sense to more people. If you are able to, please verify that I have not altered it from your intended meaning.

This post imported from StackExchange Physics at 2017-03-05 22:13 (UTC), posted by SE-user JeopardyTempest
Hi, JeopardyTempest, thanks for your editing. I quote directly from the reference in case I didn't express clearly.

This post imported from StackExchange Physics at 2017-03-05 22:13 (UTC), posted by SE-user Wilson Ko
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 :-)

This post imported from StackExchange Physics at 2017-03-05 22:13 (UTC), posted by SE-user JeopardyTempest
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.

This post imported from StackExchange Physics at 2017-03-05 22:13 (UTC), posted by SE-user FraSchelle
Hi, FraSchelle, superconducting state is not necessarily topological, could provide some reference related?

This post imported from StackExchange Physics at 2017-03-05 22:13 (UTC), posted by SE-user Wilson Ko