The investigation of the spectral and dynamical delocalization-localization (DL) transitions have revealed intriguing features in a wide expanse of non-Hermitian systems. The present study aims at exploring the spectral and the dynamical properties in a non-Hermitian quasiperiodic system with asymmetric hopping, in the presence of Rashba spin-orbit (RSO) interaction. In particular, in such systems, we have identified that the DL transition is associated with a concurrent change in the energy spectrum, where the eigenstates always break the time-reversal symmetry for all strengths of the quasiperiodic potential, contrary to the systems without RSO interaction. Furthermore, in this work, we have demonstrated that the open boundary energy spectrum in the prototypical 1D nonreciprocal lattice remains real up to a certain system size and forms complex spectral loops with an increase in the size of the lattice. We find that the skin effect remains unaltered irrespective of the nature of the spectrum. In addition, it is illustrated that the spin-flip term in the RSO interaction possesses a tendency to diminish the directionality of the skin effect. On scrutinizing the dynamical attributes in our non-Hermitian system, we unveil that in spite of the fact that the spectral DL transition accords with the dynamical phase transition, interestingly, the system acquires a nonzero transport behavior, and in fact comes across hyperdiffusive and negative diffusion dynamical regimes depending upon the strength of the RSO interaction, in the spectrally localized regime.

• Received 26 August 2022
• Accepted 3 February 2023

DOI:https://doi.org/10.1103/PhysRevB.107.064305