Spin resolved spectral topology and re-entrant localization in a non Hermitian quasiperiodic SSH chain

Abstract: We investigate localization and spectral topology in a non Hermitian quasiperiodic Su Schrieffer Heeger lattice with Rashba spin orbit coupling and spin-dependent hopping. By analyzing the inverse participation ratio, complex energy spectrum, and spectral winding numbers, we demonstrate the emergence of a re-entrant transition from extended to localized and back to extended phases as the non-Hermitian parameter increases. The localization transition is accompanied by a simultaneous real-complex-real spectral transition in the complex-energy plane. In the absence of spin dependent hopping, the spectrum forms two nearly spin-degenerate loops characterized by winding numbers w = 2. Upon introducing finite spin-dependent hopping, each loop splits into two independent spin-resolved spectral branches, resulting in four disconnected spectral contours carrying distinct winding sectors. Our results reveal a direct correspondence between localization, spectral topology, and spin-resolved spectral splitting in non-Hermitian quasiperiodic systems.