Non-Hermitian dislocation modes: Stability and melting across 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.

Published version: 6 Pages, 4 Figures (Supplemental Material: as Ancillary file)

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• Non-Hermitian skin effect of dislocations and its topological origin
• Non-Hermitian boundary spectral winding
• Erratic non-Hermitian skin localization
• A brief review of hybrid skin-topological effect
• Projected Topological Branes
• Geometry-dependent skin effect and anisotropic Bloch oscillations in a non-Hermitian optical lattice
• Making topologically trivial non-Hermitian systems nontrivial via gauge fields
• Real-space topological localizer index to fully characterize the dislocation skin effect
• Topologically distinct atomic insulators
• Emergent metallicity at the grain boundaries of higher-order topological insulators
• Quantized electrical, thermal, and spin transports of non-Hermitian clean and dirty two-dimensional topological insulators and superconductors
• Topological magnonic dislocations modes
• Hybrid symmetry class topological insulators
• Dynamic melting and condensation of topological dislocation modes
• Topological and fractal defect states in non-Hermitian lattices
• Dispersive nodal fermions along grain boundaries in Floquet topological crystals
• Experimentally Probing Non-Hermitian Spectral Transition and Eigenstate Skewness
• Zero modes and index theorems for non-Hermitian Dirac fermions
• Fragile dislocation modes in obstructed atomic topological phases
• Algebraic States in Continuum in $d>1$ Dimensional Non-Hermitian Systems
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases