Non-Hermitian skin effect of dislocations and its topological origin

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 the 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 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 fall outside of the known topological classification based on bulk-defect correspondence.

Automated summary

In two-dimensional non-Hermitian systems, dislocations can lead to density accumulation or depletion by localizing an extensive number of states. The discovery of a topological invariant responsible for the dislocation skin effect sheds light on a new aspect of non-Hermitian systems and their defects. This effect, characterized by a Z(2) Hopf index dependent on the Burgers vector, challenges the known topological classification based on bulk-defect correspondence.