Non-Hermitian Skin Effect in a Non-Hermitian Electrical Circuit.

Shuo Liu,Oubo You,Ruiwen Shao,Lei Zhang,Haotian Wu,Tie Jun Cui,Shaojie Ma,Yuan Jiang Xiang,Shuang Zhang

doi:10.34133/2021/5608038

Shuo Liu, Oubo You + Show 7 more

Open Access

https://doi.org/10.34133/2021/5608038

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Abstract

The conventional bulk-boundary correspondence directly connects the number of topological edge states in a finite system with the topological invariant in the bulk band structure with periodic boundary condition (PBC). However, recent studies show that this principle fails in certain non-Hermitian systems with broken reciprocity, which stems from the non-Hermitian skin effect (NHSE) in the finite system where most of the eigenstates decay exponentially from the system boundary. In this work, we experimentally demonstrate a 1D non-Hermitian topological circuit with broken reciprocity by utilizing the unidirectional coupling feature of the voltage follower module. The topological edge state is observed at the boundary of an open circuit through an impedance spectra measurement between adjacent circuit nodes. We confirm the inapplicability of the conventional bulk-boundary correspondence by comparing the circuit Laplacian between the periodic boundary condition (PBC) and open boundary condition (OBC). Instead, a recently proposed non-Bloch bulk-boundary condition based on a non-Bloch winding number faithfully predicts the number of topological edge states.

Highlights

Non-Hermitian systems with gain and loss are very common in the real world [1,2,3,4,5]
One of the intriguing recent discoveries is the breakdown of conventional bulk-boundary correspondence [6], a well-known principle used to predict the number of topological edge states of a finite Hermitian system with open boundary condition (OBC) directly from the topological invariant of the same system with periodic boundary condition (PBC) [7]
Yao et al explained this phenomenon as a result of the non-Hermitian skin effect (NHSE), an exponential decay behavior of eigenstates in non-Hermitian systems with broken reciprocity where most of the eigenstates are localized near the boundary

Summary

Introduction

Non-Hermitian systems with gain and loss are very common in the real world [1,2,3,4,5]. One of the intriguing recent discoveries is the breakdown of conventional bulk-boundary correspondence [6], a well-known principle used to predict the number of topological edge states of a finite Hermitian system with open boundary condition (OBC) directly from the topological invariant of the same system with periodic boundary condition (PBC) [7]. To confirm the breakdown of conventional bulk-boundary correspondence in such non-Hermitian topological circuits, we compare the differences of phase transition conditions for circuit under the PBC and OBC with both theoretical calculations and numerical simulations. We show that a recently proposed bulkboundary correspondence in the non-Hermitian regime which introduces a non-Bloch wave vector for the calculation of the topological invariant precisely predicts the number of topological edge mode in such non-Hermitian topological circuits [6]

Bulk Properties

A: ð7Þ

Topological Edge Stage in the Finite Circuit

Conclusion

Method

Conflicts of Interest