Unconventional real-complex spectral transition and Majorana zero modes in nonreciprocal quasicrystals

Abstract

Non-Hermiticity from nonreciprocal hoppings has recently been shown to induce exotic non-Hermitian phenomena. Here, we study a class of nonreciprocal quasicrystal superconductors described by one-dimensional Kitaev and dimerized Kitaev chains with complex quasiperiodic potentials. We unveil that the quasiperiodic potentials lead to a localization transition and all states become localized, but the nonreciprocal hopping is favorable to the extension of these states. We also uncover the existence of correspondence between the localization transition and the unconventional real-complex transition of the energy spectrum. Moreover, the localization transition takes place accompanied by a topological phase transition, which can be determined by calculating the energy gap closing point and topological invariants. Especially in the dimerized Kitaev chain, three distinguishable regions of the wave function are observed, i.e., an extended region, a localized region, and an intermediate region with mobility edges, which originates from the interplay between the dimerized hopping and the non-Hermitian quasiperiodic potential. In this case, the topological phase transition point is consistent with the boundary between the intermediate and localized regions. Furthermore, the dimerized hopping can induce a second localization transition, where the extended bulk states become localized and then extended again. These unusual properties provide a distinctive paradigm compared with the diagonal quasiperiodic systems.