Universal non-Hermitian skin effect in two and higher dimensions

Kai Zhang, Zhesen Yang () and Chen Fang ()
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Kai Zhang: Chinese Academy of Sciences
Zhesen Yang: Chinese Academy of Sciences
Chen Fang: Chinese Academy of Sciences

Nature Communications, 2022, vol. 13, issue 1, 1-7

Abstract: Abstract Skin effect, experimentally discovered in one dimension, describes the physical phenomenon that on an open chain, an extensive number of eigenstates of a non-Hermitian Hamiltonian are localized at the end(s) of the chain. Here in two and higher dimensions, we establish a theorem that the skin effect exists, if and only if periodic-boundary spectrum of the Hamiltonian covers a finite area on the complex plane. This theorem establishes the universality of the effect, because the above condition is satisfied in almost every generic non-Hermitian Hamiltonian, and, unlike in one dimension, is compatible with all point-group symmetries. We propose two new types of skin effect in two and higher dimensions: the corner-skin effect where all eigenstates are localized at corners of the system, and the geometry-dependent-skin effect where skin modes disappear for systems of a particular shape, but appear on generic polygons. An immediate corollary of our theorem is that any non-Hermitian system having exceptional points (lines) in two (three) dimensions exhibits skin effect, making this phenomenon accessible to experiments in photonic crystals, Weyl semimetals, and Kondo insulators.

Date: 2022
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DOI: 10.1038/s41467-022-30161-6

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