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

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.

11 pages, 8 figures

References in corpus (10)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Crystalline Insulators
• Topological Defects and Gapless Modes in Insulators and Superconductors
• The space group classification of topological band insulators
• Topological Mott Insulators
• Helical Metal Inside a Topological Band Insulator
• Genons, twist defects, and projective non-Abelian braiding statistics
• Zero-energy states bound to a magnetic pi-flux vortex in a two-dimensional topological insulator

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