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Title: Non-Hermitian skin effect in two dimensional continuous systems
Abstract

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.

 
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Award ID(s):
2012172
NSF-PAR ID:
10478982
Author(s) / Creator(s):
;
Publisher / Repository:
IOP Science
Date Published:
Journal Name:
Physica Scripta
Volume:
98
Issue:
1
ISSN:
0031-8949
Page Range / eLocation ID:
015005
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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