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Does the presence of the Aharonov-Bohm (AB) effect break Time-reversal symmetry (TRS) for spinless systems in a topological square lattice? As we know that TRS protects the edge states in Topological insulators. So TRS is somewhat essential to have non-trivial topological phases (always true?). Or there may be some points (in the units of flux quanta) where TRS still survives even if we have AB effect. How can one expect a 2D topological insulator in the presence of AB effect...a bit confused!

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