Critical non-Hermitian skin effect

Linhu Li (), Ching Hua Lee (), Sen Mu () and Jiangbin Gong ()
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Linhu Li: National University of Singapore
Ching Hua Lee: National University of Singapore
Sen Mu: National University of Singapore
Jiangbin Gong: National University of Singapore

Nature Communications, 2020, vol. 11, issue 1, 1-8

Abstract: Abstract Critical systems represent physical boundaries between different phases of matter and have been intensely studied for their universality and rich physics. Yet, with the rise of non-Hermitian studies, fundamental concepts underpinning critical systems - like band gaps and locality - are increasingly called into question. This work uncovers a new class of criticality where eigenenergies and eigenstates of non-Hermitian lattice systems jump discontinuously across a critical point in the thermodynamic limit, unlike established critical scenarios with spectrum remaining continuous across a transition. Such critical behavior, dubbed the “critical non-Hermitian skin effect”, arises whenever subsystems with dissimilar non-reciprocal accumulations are coupled, however weakly. This indicates, as elaborated with the generalized Brillouin zone approach, that the thermodynamic and zero-coupling limits are not exchangeable, and that even a large system can be qualitatively different from its thermodynamic limit. Examples with anomalous scaling behavior are presented as manifestations of the critical non-Hermitian skin effect in finite-size systems. More spectacularly, topological in-gap modes can even be induced by changing the system size. We provide an explicit proposal for detecting the critical non-Hermitian skin effect in an RLC circuit setup, which also directly carries over to established setups in non-Hermitian optics and mechanics.

Date: 2020
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DOI: 10.1038/s41467-020-18917-4

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