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I understand that a topological insulator is one with an insulating bulk and conducting surface but I don't understand why or how the topological part comes into it. All of the resources I've found don't explain the reason behind the name or how topology plays a role. Could someone offer an explanation?

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  • $\begingroup$ The word 'topological' comes into it because one performs an algebraic topology of Hamiltonians on Hilbert space (after suitable interpretation), and one finds a non-trivial set of path-connected components. $\endgroup$ – PPR Aug 4 '19 at 5:11
  • $\begingroup$ @PPR "Performs an algebraic topology of Hamiltonians on Hilbert space" is a meaningless statement. This comment does nothing but confuse the reader. $\endgroup$ – Very Confused Sep 17 '20 at 10:34
  • $\begingroup$ If "performs an algebraic topology of Hamiltonians on Hilbert space" intimidates you, you may instead think of "define a topology on the appropriate space of local insulating Hamiltonians and compute its set of path connected components." $\endgroup$ – PPR Sep 17 '20 at 14:06

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