We investigate the non-Hermitian skin effect (NHSE) and topological phases in a ladder model with staggered nonreciprocal interleg hopping, consisting of a Su-Schrieffer-Heeger chain coupled to a normal tight-binding chain. By tuning the system parameters, we show that the direction of the NHSE under open boundary conditions can be reversed and can even become energy dependent. The NHSE is further characterized by the spectral winding number under periodic boundary conditions. We also demonstrate that the interleg coupling significantly enlarges the topologically nontrivial parameter regime. Remarkably, there are two topological phases characterized by winding numbers $W=\pm 1$, with the zero-energy topological edge modes residing on different sites in the two legs. Furthermore, increasing the nonreciprocity of the interleg hopping modifies the topological phase boundaries and eventually drives the system into a topologically trivial phase. Our results establish staggered nonreciprocal interleg hopping as an effective mechanism for engineering both the non-Hermitian skin effect and topological phases in ladder systems.

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• Edge states
• Skin effect
• Topological phases of matter
• Non-Hermitian systems