Skin-Anderson Localization Transition in Strongly Coupled Disordered Non-Hermitian Chains

Abstract

The interplay between disorder and non-Hermitian effects gives rise to a variety of intriguing localization phenomena. While disorder tends to localize the eigenstates through Anderson localization, non-Hermitian non-reciprocity promotes the formation of skin modes by driving the eigenstates toward the system boundaries giving rise to non-Hermitian skin effect (NHSE). In this work, we investigate the interplay between these competing mechanisms in a two-leg ladder consisting of a Hatano-Nelson chain coupled to a Hermitian chain via asymmetric inter-chain hopping, with strong disorder present in both chains. We show that tuning the asymmetry of the inter-chain coupling induces successive transitions in the nature of the eigenstates, from skin localization to Anderson localization and subsequently back to skin localization. Remarkably, the non-Hermitian skin effect re-emerges even though the energy spectrum exhibits a line-gap topology, demonstrating that robust skin localization can persist beyond the conventional point-gap regime.