Non-hermitian second-order topological superconductor with $$s_\pm $$ s ± -wave pairing

Non-Hermitian systems exhibit many exotic phenomena without any Hermitian counterpart, such as the non-Hermitian skin effect, which can fundamentally change the topology of the systems. In this paper, we investigate the topology of the non-Hermitian superconductor with $$s_\pm $$ s ± -wave pairing. The study of $$s_\pm $$ s ± -wave pairing is crucial for understanding unconventional superconductivity in iron-based materials, as it explains the sign reversal gap driven by spin fluctuations. This mechanism offers insights into other correlated electron systems, such as nickelates under high pressure, and advances the field of high-temperature superconductivity. We explore the topological features of a non-Hermitian superconductor with $$s_\pm $$ s ± -wave pairing on a square lattice. We demonstrate that non-Hermitian second-order topological superconductors exhibit unique band collapse behaviors and localized Majorana corner and zero modes under open boundary conditions. Furthermore, we reveal the system’s $$Z_2$$ Z 2 skin effect, preserving particle-hole symmetry and providing insights into topological phase transitions between non-Hermitian second-order topological superconductors and trivial superconductors. Graphic abstract