Speaker
Description
It is often accepted that the Zak phase of one-dimensional topological insulators corresponds to the number of edge states. However, the Zak phase fails to predict edge states in some cases, and when it does its prediction depends on the choice of unit cell. We provide a derivation of bulk-boundary correspondence that successfully predicts the number of edge states in semi-infinite chains, topological and non-topological, using the zeroes of components of the analytically extended Bloch wavefunction. Furthermore, we interpret symmetry-protected topological edge states as exceptional points of the analytically extended Bloch Hamiltonian. The derived bulk-boundary correspondence closely resembles known results, but does not rely on involved mathematics, as is often the case with K-theory. Our expression explicitly depends on the boundary, it thus does not fix the issue of the Zak phase depending on the choice of unit cell. Finally, our Bulk-Boundary correspondence can be applied for computing edge and corner states in two-dimensional topological insulators.
| Keyword-1 | Topological insulators |
|---|---|
| Keyword-2 | Edge states |
| Keyword-3 | Theory |