Non-Hermitian skin effect in two dimensional continuous systems

An extensive number of the eigenstates can become exponentially localized at one boundary of nonreciprocal non-Hermitian systems. This effect is known as the non-Hermitian skin effect and has been studied mostly in tight-binding lattices. To extend the skin effect to continues systems beyond 1D, we...

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Bibliographic Details
Published in:Physica scripta 2023-01, Vol.98 (1), p.15005
Main Authors: Yuce, C, Ramezani, H
Format: Article
Language:English
Subjects:
nonhermitian skin effect
nonhermitian topological phase
spectral topology
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Summary:An extensive number of the eigenstates can become exponentially localized at one boundary of nonreciprocal non-Hermitian systems. This effect is known as the non-Hermitian skin effect and has been studied mostly in tight-binding lattices. To extend the skin effect to continues systems beyond 1D, we introduce a quadratic imaginary vector potential in the continuous two dimensional Schrödinger equation. We find that inseparable eigenfunctions for separable nonreciprocal Hamiltonians appear under infinite boundary conditions. Introducing boundaries destroy them and hence they can only be used as quasi-stationary states in practice. We show that all eigenstates can be clustered at the point where the imaginary vector potential is minimum in a confined system.
ISSN:0031-8949
1402-4896
DOI:10.1088/1402-4896/aca43b