Non-Hermitian dislocation modes: Stability and melting across exceptional points

TL;DR

This paper demonstrates that dislocation defects in non-Hermitian topological systems host robust modes immune to skin effects, but these modes melt at exceptional points, offering a new way to probe non-Hermitian topology.

Contribution

It reveals that dislocation modes in non-Hermitian systems are robust against skin effects and can be used to probe NH topology, especially near exceptional points.

Findings

Dislocation modes are immune to skin effects in NH systems.

Dislocation modes support robust topological states in NH systems with band inversion.

Dislocation modes melt into system boundaries at exceptional points.

Abstract

The traditional bulk-boundary correspondence assuring robust gapless modes at the edges and surfaces of insulating and nodal topological materials gets masked in non-Hermitian (NH) systems by the skin effect, manifesting an accumulation of a macroscopic number of states near such interfaces. Here we show that dislocation lattice defects are immune to such skin effect or at most display a \emph{weak} skin effect (depending on its relative orientation with the Burgers vector), and as such they support robust topological modes in the bulk of a NH system, specifically when the parent Hermitian phase features band inversion at a finite momentum. However, the dislocation modes gradually lose their support at their core when the system approaches an exceptional point, and finally melt into the boundary of the system across the NH band gap closing. We explicitly demonstrate these findings for a two-dimensional NH Chern insulator, thereby establishing that dislocation lattice defects can be instrumental to experimentally probe pristine NH topology.