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arXiv · 1908.01553

Hidden Chern number in one-dimensional non-Hermitian chiral-symmetric systems

Wojciech Brzezicki·Timo Hyart
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Abstract

We consider a class of one-dimensional non-Hermitian models with a special type of a chiral symmetry which is related to pseudo-Hermiticity. We show that the topology of a Hamiltonian belonging to this symmetry class is determined by a hidden Chern number described by an effective 2D Hermitian Hamiltonian $H^{\rm eff} (k, η)$, where $η$ is the imaginary part of the energy. 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.

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Wojciech Brzezicki, Timo Hyart. 2019-10-09. Hidden Chern number in one-dimensional non-Hermitian chiral-symmetric systems. https://doi.org/10.1103/physrevb.100.161105

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