Restoration of non-Hermitian bulk-boundary correspondence by counterbalancing skin effect

In systems exhibiting the non-Hermitian skin effect (NHSE), the bulk spectrum under open boundary conditions (OBC) significantly differs from that of its periodic counterpart. This disparity renders the conventional bulk-boundary correspondence (BBC) inapplicable. Here we propose an intuitive approach called doubling and swapping to restore the BBC, using the non-Hermitian Su-Schrieffer-Heeger model as an example. Explicitly, we construct a modified system free of NHSE by swapping the asymmetric intracell hoppings in every second primitive unit cell. Importantly, this change does not alter the OBC spectrum. As a result, the modified periodic system can serve as the bulk for defining topological invariants that accurately predict edge states and topological phase transitions. The basic principle is applicable to many other systems. By extending the study to disordered systems in which the asymmetric hoppings are randomly swapped, we show that two types of winding numbers can also be defined to account for the NHSE and topological edge states, respectively.