Stability of the Non-Hermitian Skin Effect in One Dimension
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Date
2024-08
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Journal Article
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Abstract
This paper shows both analytically and numerically that the skin effect in systems of non-Hermitian subwavelength resonators is robust with respect to random imperfections in the system. The subwavelength resonators are highly contrasting material inclusions that resonate in a low-frequency regime. The non-Hermiticity is due to the introduction of a directional damping term (motivated by an imaginary gauge potential), which leads to a skin effect that is manifested by the system's eigenmo des accumulating at one edge of the structure. We elucidate the topological protection of the associated (real) eigenfrequencies and illustrate numerically the competition between the two different localization effects present when the system is randomly perturbed: the non-Hermitian skin effect and the disorder-induced Anderson localization. We show numerically that, as the strength of the disorder increases, more and more eigenmo des become localized in the bulk. Our results are based on an asymptotic matrix model for subwavelength physics and can be generalized also to tight-binding models in condensed matter theory.
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published
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Journal / series
Volume
84 (4)
Pages / Article No.
1697 - 1717
Publisher
SIAM
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Subject
non-Hermitian systems; non-Hermitian skin effect; subwavelength resonators; imaginary gauge potential; Toeplitz matrix; eigenvector condensation; Anderson localization; stability analysis; disorder-induced phase transition
Organisational unit
09504 - Ammari, Habib / Ammari, Habib
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Funding
200307 - Mathematics of dielectric artificial media (SNF)