Localization transitions in a non-Hermitian quasiperiodic lattice

The delocalization-localization (DL) transition in non-Hermitian systems is a fascinating phenomenon with distinct characteristics compared to their Hermitian counterparts. In our study, we deal with the DL transition in a generalized non-Hermitian lattice. The non-Hermitian behavior arises due to asymmetry in the hoppings and the complex nature of the quasiperiodic (QP) potentials. We demonstrate that the interplay between these two leads to more diverse and intricate phases. For identical modulation of the real and the complex parts of the QP potential, we obtain the analytical expression of the critical point that precisely captures the DL transition for systems with periodic boundary conditions (PBC). Our numerical investigations reveal that the critical point remains unchanged even with open boundary conditions (OBC). One particularly fascinating aspect of our findings is the emergence of a mixed phase between the delocalized and localized regions in systems with nonidentical modulation of the real and complex parts of the QP potential. This mixed phase presents a remarkable coexistence of skin modes and localized states for systems with OBC, while systems with PBC exhibit a coexistence of delocalized and localized states within the mixed phase. To provide further insights into the underlying physics, we construct comprehensive phase diagrams, shedding light on the crucial role of various parameters in a broad range of non-Hermitian QP lattices.