Non-Hermitian Chern bands

TL;DR

This paper reveals that in non-Hermitian systems, traditional bulk-boundary correspondence based on Chern numbers fails due to the non-Bloch nature of eigenstates, leading to the development of non-Bloch Chern numbers that accurately predict edge modes.

Contribution

It introduces non-Bloch Chern numbers to correctly describe topological properties of non-Hermitian bands, overcoming limitations of conventional Bloch-based invariants.

Findings

Non-Hermitian skin effect causes deviations from Bloch theory.

Non-Bloch Chern numbers predict chiral edge modes accurately.

Phase diagrams differ significantly from Bloch predictions in non-Hermitian systems.

Abstract

The relation between chiral edge modes and bulk Chern numbers of quantum Hall insulators is a paradigmatic example of bulk-boundary correspondence. We show that the chiral edge modes are not strictly tied to the Chern numbers defined by a non-Hermitian Bloch Hamiltonian. This breakdown of conventional bulk-boundary correspondence stems from the non-Bloch-wave behavior of eigenstates (non-Hermitian skin effect), which generates pronounced deviations of phase diagrams from the Bloch theory. We introduce non-Bloch Chern numbers that faithfully predict the numbers of chiral edge modes. The theory is backed up by the open-boundary energy spectra, dynamics, and phase diagram of representative lattice models. Our results highlight a unique feature of non-Hermitian bands and suggest a non-Bloch framework to characterize their topology.