Topological phase transitions and non-Hermitian skin effect in a Kitaev chain with complex commensurate modulations

We systematically investigate the Kitaev chain with the complex commensurate modulations of the on-site chemical potential, nearest-neighbor hopping amplitude, and nearest-neighbor pairing strength. We observe that the topological phase transition point remains unaltered when subjected to the purely imaginary modulation of the on-site chemical potential. Moreover, the corresponding phase factor can induce a topologically nontrivial phase, characterized by the topological invariant obtained through the transfer matrix method. Furthermore, the complex modulation of the hopping amplitude is conducive to the topologically nontrivial phase, but the complex modulation of the pairing strength is unfavorable for it. Unexpectedly, the non-Hermitian skin effect is observed in the presence of complex modulations of both the chemical potential and pairing strength. It is noteworthy that the non-Hermitian skin effect is enhanced with an increase of the complex modulation of the pairing strength while is weakened through the complex modulation of the hopping amplitude. Our investigation provides a path to elucidate the non-Hermitian skin effect induced by the complex modulations rather than the nonreciprocity in topological superconductors.