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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See Reconciling topological insulators and topological order and “Topological” notions in physics. – Anyon Jun 23 '19 at 18:29
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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. – PPR Aug 04 '19 at 05:11
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@PPR "Performs an algebraic topology of Hamiltonians on Hilbert space" is a meaningless statement. This comment does nothing but confuse the reader. – AmorFati Sep 17 '20 at 10:34
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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." – PPR Sep 17 '20 at 14:06