$\mathcal{PT}$ and anti-$\mathcal{PT}$ phase transitions in a trimerized Su--Schrieffer--Heeger chain with nonreciprocal Rashba spin-orbit coupling

Abstract:We theoretically investigate a one-dimensional trimerized Su--Schrieffer--Heeger chain with three sublattices per unit cell subjected to a nonreciprocal Rashba spin-orbit coupling. Invoking a spin-flip symmetry, the non-Hermitian Hamiltonian decomposes into two independent spin sectors, enabling a spin-resolved analysis of non-Hermitian skin effects and system symmetries. We identify a rich phase diagram consisting of four bulk phases and two edge-state phases. The bulk phases include fully $\mathcal{PT}$-unbroken (real-spectrum) and fully anti-$\mathcal{PT}$-unbroken (imaginary-spectrum) regimes, as well as two mixed phases where one band remains on the real or imaginary axis while the other two form complex-conjugate pairs. The two edge-state phases correspond to topological edge modes with either $\mathcal{PT}$-unbroken (real) or anti-$\mathcal{PT}$-unbroken (imaginary) energies. Using non-Bloch band theory and Cardano's method, we derive closed-form expressions for phase boundaries and establish the bulk-edge correspondence for each spin sector. Calculations of Berry phase and directional inverse participation ratios confirm our analytical predictions. Our results provide a minimal platform for realizing spin-resolved non-Hermitian topology and edge-selective symmetry preservation, in which the bulk and edge states belong to distinct symmetry classes.

Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Physics (quant-ph)

arXiv:2608.20520 [cond-mat.mes-hall]

(or arXiv:2608.20520v1 [cond-mat.mes-hall] for this version)

https://doi.org/10.48550/arXiv.2608.20520 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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