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Description

Topological insulators are insulating phases of matter distinguished by non-trivial topological invariants. A striking feature arises when two insulators with distinct invariants are joined: conducting states emerge along their interface, a phenomenon known as the bulk–edge correspondence (BEC). In this talk, we investigate qualitative BEC for Fermionic time-reversal-invariant topological insulators, characterized by the Z_2-valued Fu–Kane–Mele index, with particular attention to curved interfaces. We will begin with Chern insulators, classified by their Chern numbers, and then extend the discussion to Z_2 topological insulators. In particular, we

will highlight how the seemingly contradictory properties of translation invariance and local determinacy in Z_2 insulators naturally arise from different formulations of the index.