Impurity Bound States and Greens Function Zeroes as Local Signatures of Topology

TL;DR

This paper demonstrates that the local in-gap Greens function eigenvalues reveal the topological phase of insulators, with zeros indicating nontrivial topology and enabling experimental detection via impurity bound states.

Contribution

It introduces a novel local Greens function criterion for topological classification, linking eigenvalue zeros to impurity-bound states in insulators.

Findings

Eigenvalues of local Greens function attain zeros in topological insulators.

Zeros in Greens function eigenvalues correspond to in-gap bound states.

Method allows experimental detection of 2D topological phases.

Abstract

We show that the local in-gap Greens function of a band insulator $\mathbf{G}_0 (\epsilon,\mathbf{k}_{\parallel},\mathbf{r}_{\perp}=0)$, with $\mathbf{r}_\perp$ the position perpendicular to a codimension-1 or -2 impurity, reveals the topological nature of the phase. For a topological insulator, the eigenvalues of this Greens function attain zeros in the gap, whereas for a trivial insulator the eigenvalues remain nonzero. This topological classification is related to the existence of in-gap bound states along codimension-1 and -2 impurities. Whereas codimension-1 impurities can be viewed as 'soft edges', the result for codimension-2 impurities is nontrivial and allows for a direct experimental measurement of the topological nature of 2d insulators.