Spatial separation of skin and edge states in non-Hermitian double-chain systems with unidirectional coupling

In non-Hermitian systems, bulk states typically localize at the same edge as edge states, rendering this phenomenon a central focus in non-Hermitian topological physics. Here, we investigate the double-chain Su–Schrieffer–Heeger model with unidirectional interchain coupling and propose a method to simulate the model through a unidirectional circuit design employing voltage followers. It is particularly intriguing that by employing the directional inverse participation ratio, we establish a clear distinction between bulk and edge states, which arises from their fundamentally different localization behaviors: bulk states exhibit directional localization due to the competition between the strength of intracell and intercell hoppings, while edge states demonstrate unilateral localization as the dominance of non-Hermiticity. Furthermore, our numerical results for the skin phase transition show excellent agreement with analytical solution derived from the eigenenergy spectrum, revealing the boundaries of spatial separation. Notably, the system manifests a bipolar skin effect when dissipation is introduced to intracell hopping, with this effect being quantitatively characterized through skin polarity. Our findings significantly advance the understanding of eigenstate localization behavior and unveil richer physical properties inherent in special nonreciprocal models.