Tunable non-Hermitian skin effect and topological phases in ladders with staggered nonreciprocal inter-leg hopping

This paper investigates the interplay between the non-Hermitian skin effect (NHSE) and topological phases in a ladder system. The model consists of two coupled one-dimensional chains: an Su-Schrieffer-Heeger (SSH) chain and a uniform tight-binding chain. The key innovation is the introduction of staggered nonreciprocal inter-leg hopping, which alternates between odd and even sites. This specific coupling mechanism allows for precise control over the localization of eigenstates and the topological properties of the system.

The authors show that the staggered nonreciprocity is a sufficient condition to induce the NHSE. By tuning the hopping parameters, the direction of the skin effect—where eigenstates accumulate at the boundaries—can be reversed. Remarkably, the system can transition into a regime where the NHSE becomes energy-dependent, meaning eigenstates at different energy levels accumulate at opposite ends of the ladder. This behavior is characterized by the spectral winding number of the periodic boundary condition (PBC) spectrum, which provides a topological explanation for the observed localization.

The coupling between the SSH chain and the uniform chain significantly enlarges the parameter space where topologically nontrivial phases exist compared to an isolated SSH chain. The authors identify zero-energy edge modes that are localized on specific legs of the ladder. These modes are characterized by real-space winding numbers of $W = \pm 1$. The study further reveals that increasing the nonreciprocity of the inter-leg hopping eventually drives the system into a topologically trivial phase, demonstrating that nonreciprocity acts as a control parameter for both the skin effect and the topological state of the system.