Anatomy of skin modes and topology in non-Hermitian systems

Non-Hermitian systems can exhibit a counterintuitive phenomenon where a single local boundary or disorder modifies the entire spectrum, no matter how large the system is. In such cases, all bulk modes become localized ``skin'' modes, and usual bulk topological invariants no longer correctly predict topological boundary modes. Generalizing Laughlin's gauge argument to complex fluxes, the authors derive a geometrical approach for the exact determination of the skin-mode spectrum. They also devise a new topological criterion for non-Hermitian particle-hole symmetric Hamiltonians based on complex analysis.