Non-Hermitian skin effect of dislocations and its topological origin

TL;DR

This paper reveals that dislocations in two-dimensional non-Hermitian systems can cause localized density changes, driven by a topological invariant, independent of system boundaries, expanding the understanding of non-Hermitian skin effects.

Contribution

It introduces a topological invariant, a ${\mathbb Z}_2$ Hopf index, that explains dislocation-induced skin effects in non-Hermitian systems, distinct from known classifications.

Findings

Dislocations cause density accumulation or depletion in 2D non-Hermitian systems.

The effect is characterized by a ${\mathbb Z}_2$ Hopf index related to Burgers vectors.

This phenomenon extends the topological understanding beyond bulk-boundary correspondence.

Abstract

We demonstrate that dislocations in two-dimensional non-Hermitian systems can give rise to density accumulation or depletion through the localization of an extensive number of states. These effects are shown by numerical simulations in a prototype lattice model and expose a different face of non-Hermitian skin effect, by disentangling it from the need for boundaries. We identify a topological invariant responsible for the dislocation skin effect, which takes the form of a ${\mathbb Z}_2$ Hopf index that depends on the Burgers vector characterizing the dislocations. Remarkably, we find that this effect and its corresponding signature for defects in Hermitian systems falls outside of the known topological classification based on bulk-defect correspondence.