Topological phase and skin effect in a non-Hermitian dimerized Kitaev model

We investigate the non-Hermitian dimerized Kitaev model with intracell and intercell nonreciprocal hopping. In the Hermitian case, the topologically nontrivial phase region expands with increasing on-site potentials when the two sublattices have the same sign, but shrinks when their signs differ. When nonreciprocal hopping is introduced and on-site potentials share the same sign, the topologically nontrivial phase region gradually narrows as the nonreciprocity grows, accompanied by the emergence of the non-Hermitian skin effect–mainly dominated by intracell nonreciprocity. The skin direction characterized by the spectral winding number, correlates with the real part of the energy spectrum, which displays a Z₂ character protected by particle-hole symmetry. Conversely, when on-site potentials have opposite signs, the topological phase region widens with increasing nonreciprocity up to a critical value, beyond which it splits into two branches. Notably, the skin effect vanishes because opposite on-site potentials induce skin effects in opposing directions, balancing the system and allowing a topological phase to emerge. Our result provides a strategy for controlling the appearance and disappearance of the non-Hermitian skin effect by tuning on-site potentials in dimerized topological superconductors.