Topological boundaries in non-Hermitian p-wave Kitaev chains with Rashba spin-orbit coupling

TL;DR

This work analyzes how Rashba spin-orbit coupling (RSOC) and non-Hermiticity reshape topological phase boundaries in a spinful one-dimensional p-wave Kitaev chain, considering uniform gain/loss and complex quasiperiodic on-site potentials. It derives an analytical ellipse boundary for the uniform NH case, showing RSOC shrinks the NH topological region, and uses numerical spectra and real-space winding to validate the prediction. For the quasiperiodic NH potential, transfer matrix and Lyapunov exponent analyses yield a boundary $|V| = 2 e^{-h}(J + \bar{\Delta})$, with RSOC again reducing the topological span; numerical phase diagrams and winding numbers corroborate. Overall, the results illuminate the cooperative effects of non-Hermiticity and RSOC on 1D topological superconductivity, with potential relevance to Rashba nanowires and open-system platforms.

Abstract

In this work, we investigate the combined effects of Rashba spin-orbit coupling (RSOC) and non-Hermiticity on topological phase transitions in spinful p-wave Kitaev chains. While previous studies have separately examined non-Hermitian (NH) extensions of Kitaev chains and the effects of RSOC in Hermitian systems, the interplay between these two mechanisms remains largely 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 potential. 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. Notably, we find that 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 topological phase transitions in both cases and validate our predictions through numerical calculations of energy spectra and real-space winding numbers. This work provides a comprehensive understanding of how non-Hermiticity and RSOC cooperatively reshape topological phase diagrams in one-dimensional superconducting systems.

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