Concurrent skin-scale-free localization and criticality under Möbius boundary conditions in a non-Hermitian ladder
Phys. Rev. B 112, 075107 – Published 4 August, 2025
DOI: https://doi.org/10.1103/nnpf-8pxq
Abstract
Non-Hermitian systems possess exotic localization phenomena beyond their Hermitian counterparts, exhibiting massive accumulation of eigenstates at the system boundaries with different scaling behaviors. In this study we investigate two weakly coupled non-Hermitian Hatano-Nelson chains under Möbius boundary conditions (MBCs) and reveal the coexistence of two distinct localization behaviors for eigenstates, namely, eigenstates exhibit non-Hermitian skin effect in one chain and scale-free localization in the other. Notably, the localization characteristics of eigenstates can be exchanged between the two chains, depending on their eigenenergies. This phenomenon is found to emerge from the critical behaviors induced by the weak interchain coupling, which can even be enhanced by MBCs in comparison to the system under other boundary conditions. Our findings deepen the understanding of non-Hermitian localization and criticality and offer insights into engineering tunable edge-localized states in synthetic quantum systems.
