Erratic Non-Hermitian Skin Localization

A novel localization phenomenon, termed erratic non-Hermitian skin localization, has been identified in disordered globally reciprocal non-Hermitian lattices. Unlike conventional non-Hermitian skin effect and Anderson localization, it features macroscopic eigenstate localization at irregular, disorder-dependent positions with subexponential decay. Using the Hatano-Nelson model with disordered imaginary gauge fields as a case study, this effect is linked to stochastic interfaces governed by the universal order statistics of random walks. Finite-size scaling analysis confirms the localized nature of the eigenstates. This discovery challenges conventional wave localization paradigms, offering new avenues for understanding and controlling localization phenomena in non-Hermitian physics.