Higher-winding phases in one-dimensional non-Hermitian topological superconductors
Non-Hermitian topological superconductors provide a setting in which point-gap topology, non-Hermitian skin effects, and Majorana zero modes are strongly intertwined. In this work, we adopt a coefficient-based approach for computing winding numbers and deriving analytical expressions for phase boundaries in one-dimensional non-Hermitian topological superconductors characterized by point-gap topology with $\mathbb{Z}$ invariants. We apply this approach to two non-Hermitian topological superconducting lattice models, with and without sublattice degrees of freedom, including longer-range hoppings, thereby accessing a much broader parameter space. These extensions generate higher-order polynomials and support phases with higher winding numbers, reflecting the underlying $\mathbb{Z}$ topology. We further clarify how a weak perturbation suppresses the non-Hermitian skin effect while preserving the sublattice-symmetry-protected invariant associated with Majorana zero modes. The predicted winding numbers are verified by open-boundary spectra, where one or multiple pairs of zero-energy boundary modes appear consistently with the bulk invariant. We also examine the stability of these modes against onsite disorder by examining the zero-mode energy, the bulk gap, and the inverse participation ratio. Our results provide a systematic and efficient route to constructing topological phase diagrams for higher-winding non-Hermitian topological superconductors.