Highly antisymmetric scale-free skin effects in coupled four-layer Hatano-Nelson models
Phys. Rev. B 114, 034105 – Published 6 July, 2026
DOI: https://doi.org/10.1103/qwqd-d2nf
Abstract
The non-Hermitian skin effect is an intriguing phenomenon that initially emerges in non-Hermitian systems featuring nonreciprocal hoppings. In such settings, eigenstates tend to accumulate predominantly at one end of the lattice chain under open boundary conditions. However, the localization length of these skin states remains fixed and is independent of the lattice size. Here, we demonstrate a distinct type of skin effect in a coupled four-layer Hatano-Nelson model, where the localization length scales inversely with the lattice size, even in the presence of weak interlayer coupling. Notably, we find that every two chains sharing the same complex potentials form identical loops in the complex energy plane. Moreover, all eigenstate profiles are antisymmetrically distributed across two pairs of double chains, provided their nonreciprocal hoppings are opposite in direction. Our results reveal that scale-free skin effects can be engineered by both on-site potentials and nonreciprocity, offering new avenues for exploring scale-free skin effects in multichain non-Hermitian systems.
