Topological invariants for non-Hermitian chiral-symmetric systems

We show that the topology of one-dimensional chiral-symmetric non-Hermitian systems is determined by a hidden Chern number described by an effective 2D Hermitian Hamiltonian H_eff(k,η), where k is the momentum and η is the imaginary part of the energy [1]. This Chern number manifests itself as topologically protected in-gap end states at zero real part of the energy. We show that the bulk-boundary correspondence coming from the hidden Chern number is robust and immune to non-Hermitian skin effect. We introduce a minimal model Hamiltonian supporting topologically nontrivial phases in this symmetry class, derive its topological phase diagram and calculate the end states originating from the hidden Chern number. We discuss various generalizations and realizations of this model, and the corresponding topological invariants.

[1] W. Brzezicki and T. Hyart, Phys. Rev. B 100, 161105(R) (2019).