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

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