Non-Hermitian Chern bands

Shunyu Yao; Fei Song; Zhong Wang

doi:10.1103/physrevlett.121.136802

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arXiv · 1804.04672

Non-Hermitian Chern bands

Shunyu Yao·Fei Song·Zhong Wang

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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.

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Shunyu Yao, Fei Song, Zhong Wang. 2018-09-25. Non-Hermitian Chern bands. https://doi.org/10.1103/physrevlett.121.136802

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