Non-Hermitian second-order topological superconductors

Abstract: The topology of non-Hermitian systems is fundamentally changed by the non-Hermitian skin effect, which leads to the generalized bulk-boundary correspondence. Based on the non-Bloch band theory, we get insight into the interplay between the non-Hermiticity and the second-order topological superconductors in two spatial dimensions. We investigate that the non-Hermiticity drives both the bulk states and topological edge modes to accumulate toward opposite corners of the system depending on the particle and hole degrees of freedom protected by the particle-hole symmetry. Furthermore, the degeneracy of the Majorana corner modes can be broken in terms of both the eigenenergies and the eigenstates. Through an edge theory analysis, we elucidate the impact of non-Hermiticity and enable the extension of higher-order topological superconductors to the realm of non-Hermitian systems. We show that $Z_2$ skin effect and $Z_2$ skin-topological modes reveal the universal characteristics of non-Hermitian second-order topological superconductors and the generalized bulk-boundary correspondence is further enriched by the particle-hole symmetry.