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The non-Hermitian skin effect (NHSE) undermines the conventionalbulk-boundary correspondence (BBC) since it results in a distinct bulk spectrumin open-boundary systems compared to the periodic counterpart. Using thenon-Hermitian (NH) Su-Schrieffer-Heeger (SSH) model as an example, we proposean intuitive approach, termed ``doubling and swapping" method, to restore theBBC. Explicitly, we construct a modified system by swapping the asymmetricintracell hoppings in every second primitive unit cell, such that it hasdouble-sized unit cells compared to the NH SSH model and is free of NHSE.Importantly, the modified system and the NH SSH chain exhibit identical spectraunder open boundary conditions (OBC). As a result, the modified system canserve as the valid bulk for defining topological invariants that correctlypredicts edge states and topological phase transitions. The basic principle isapplicable to many other systems such as the non-Hermitian Creutz ladder model.Furthermore, we extend the study to disordered systems in which the asymmetrichoppings are randomly swapped. We show that two types of winding numbers can bedefined to account for the NHSE and topological edge states, respectively.

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