Detachment between edge and skin states in a non-Hermitian lattice

The integration of nonreciprocal non-Hermiticity and topological lattice systems can induce the emergence of the non-Hermitian skin effect, enabling a clear distinction between the behaviors of bulk states in non-Hermitian systems and those in Hermitian systems. Specifically, we focus on examining the localized directions of eigenstates in an odd-sized Su-Schrieffer-Heeger-type lattice with intracell nonreciprocal hopping, and identify a notable phenomenon of detachment between the edge and bulk states, which stands in stark contrast to the behaviors observed in even-sized cases. The localized directions of the bulk and edge states are respectively subjected to the non-Hermitian skin effect and isolated site induced by the odd size of the lattice, resulting in the detachment between the edge and skin states. To provide a comprehensive understanding of the detachment phenomenon, we present analytical solutions that illustrate the localized directions of the edge and skin states whose results are in perfect agreement with the numerical findings. Furthermore, we demonstrate that a pair of eigenstates exhibiting opposite localized directions to the skin states can appear in a trimer non-Hermitian lattice, indicating the possibility of detachment between the edge and skin states in multimer non-Hermitian lattices as well.