Non-Hermitian pseudo mobility edge in a coupled chain system

In this work, we explore interesting consequences arising from the coupling between a clean non-Hermitian chain with skin localization and a delocalized chain of the same length under various boundary conditions (BCs). We reveal that in the ladder with weak rung coupling, the non-Hermitian skin localization could induce a pseudo mobility edge (ME) in the complex energy plane, which separates states with extended and localized profiles yet allows unidirectional transport of signals. We also demonstrate the gradual takeover of the non-Hermitian skin effect in the entire system with the increase of the rung coupling under conventional open BC (OBC). When taking OBC for the non-Hermitian chain and periodic BC (PBC) for the other, it is discovered that a quantized winding number defined under PBC could characterize the transition from the pseudo-ME to the trivial extended phases, establishing a ``bulk-defect correspondence'' in our quasi-1D non-Hermitian system. This work hence unveils more subtle properties of non-Hermitian skin effects and sheds light on the topological nature of the non-Hermitian localized modes in the proximity to systems with dissimilar localization properties.