Topological in-gap states in a non-Hermitian quasicrystal with p-wave pairing

Abstract

The interplay of onsite quasiperiodic potential, superconductivity, and non-Hermiticity is explored in a non-Hermitian unconventional superconducting quasicrystal described by the Aubry-André-Harper model with 𝑝 -wave pairing. Importantly, here the asymmetry is introduced in the hopping to break the reciprocity, leading to the explicit breaking of particle-hole symmetry. In the zero-pairing limit, the model hosts an exact triple-phase transition where the topological, metal-insulator, and real-to-complex spectral transitions coincide. With weak (perturbative) pairing, this coincidence survives only approximately and is progressively destroyed as the pairing strength increases. Additionally, instead of the Majorana zero modes (MZMs) found in the symmetric hopping case, we observe the emergence of in-gap states under open boundary conditions. These in-gap states are robust against disorder, underscoring their topological protection. Therefore, unlike the MZMs, which are very challenging to experimentally realize, these in-gap states can be used in topological quantum computational protocols.