Topological boundaries in non-Hermitianp-wave Kitaev chains with Rashba spin-orbit coupling.

In this work, we investigate the combined effects of Rashba spin-orbit coupling (RSOC) and non-Hermiticity on topological phase transitions (TTs) in spinful-wave Kitaev chains. While non-Hermitian extensions of spinless Kitaev chains and the role of RSOC in Hermitian superconducting systems have been extensively studied, the influence of RSOC on topological phase boundaries in non-Hermitian spinful-wave Kitaev chains remains unexplored. We analyze this interplay by considering two distinct types of complex on-site potentials: (i) a uniform gain/loss term and (ii) a complex quasiperiodic one. We demonstrate that the impact of RSOC is highly model-dependent. In particular, RSOC does not affect the topological phase boundary in the Hermitian limit of the uniform gain/loss model (provided the spin-flip hopping is weaker than the pairing strength), but significantly alters the topological landscape in the NH regime. In contrast, for the quasiperiodic model, RSOC modifies the phase boundaries in both the Hermitian and non-Hermitian cases. We show that RSOC effectively renormalizes the superconducting pairing strength to an effective value, thereby providing a direct tuning mechanism for the size of the topological phase. Moreover, the combined interplay of non-Hermiticity and RSOC drives topological transitions at significantly lower potential strengths compared to the Hermitian limit. We derive analytical expressions for the TTs in both cases and validate our predictions through numerical calculations of energy spectra, probability distribution and real-space winding numbers. Our results reveal two distinct mechanisms by which RSOC influences topology in non-Hermitian superconductors: momentum-space gap closing in the uniform-potential case and real-space localization transitions in the quasiperiodic case. This work therefore provides a comprehensive understanding of how non-Hermiticity and RSOC cooperatively reshape topological phase diagrams in one-dimensional superconducting systems.