Non-Hermitian Aubry-André-Harper model with short- and long-range p-wave pairing

Abstract

We investigate a non-Hermitian Aubry-Andre-Harper model, considering both the short- and long-range p-wave pairing. Here, the non-Hermiticity is considered at the onsite potential. A comprehensive analysis of several critical aspects of this system, including the eigenspectra, localization properties, PT} symmetry, real to complex transition, and topological properties, is conducted. Specifically, we observe the emergence of Majorana zero modes in the case of short-range pairing, whereas the massive Dirac modes emerge in the case of long-range pairing. Notably, a triple-phase transition is identified, involving simultaneous transitions from extended or metallic state to critical multifractal state, unbroken to broken PT symmetry, and unconventional real to complex energies. In addition, a double-phase transition is observed, where the topological and superconducting transitions occur concurrently. These intriguing double- and triple-phase transitions are observed in both short- and long-range pairing cases.