Non-Hermitian topology driven by an identity term: An exactly solvable paradigm
Phys. Rev. B 114, 245102 – Published 2 October, 2026
DOI: https://doi.org/10.1103/2rld-db9c
Abstract
An identity term in the Hamiltonian is conventionally regarded as spectrally inert; it shifts energies but does not alter eigenstate topology. We show that under non-Hermitian skin pumping, this paradigm fails: a momentum-dependent identity term actively deforms the generalized Brillouin zone, thereby challenging established topological criteria that rely on fixed complex contours. Here, by introducing spin-orbit coupling into a Hatano-Nelson chain, we present an exact analytical solution for the entire non-Hermitian eigensystem under open boundary conditions. Our solution reveals how intercell spin-orbit coupling, synergizing with this nontrivial identity term, induces topological edge states and robust zero modes in the complete absence of chiral symmetry. This work establishes an exactly solvable paradigm for non-Hermitian topology beyond symmetry protection, and provides a rigorous benchmark for testing topological invariants in systems with momentum-dependent identity terms.
