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Topological insulators in three spatial dimensions are known to possess a precise bulk/boundary correspondence, in that there is a one-to-one correspondence between the 5 classes characterized by bulk topological invariants and Dirac hamiltonians on the boundary with symmetry protected zero modes.
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Note that the use of the word “chiral” here is different from the terminology of AZ. In the AZ classification, classes AIII, BDI, and CII were collectively referred to as chiral classes
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Only when V − V_{-} and A y A_{y} commute does Eq. ( 12
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