Signature of edge states in resonant wave scattering

TL;DR

This paper demonstrates how resonant wave scattering can be used to detect edge states and identify the topology of both Hermitian and non-Hermitian systems, using theoretical analysis and numerical simulations.

Contribution

It establishes a connection between eigenstates and scattering amplitudes, proposing a novel method for topological edge state detection in various systems.

Findings

Edge states can be detected via resonant scattering signatures.

The method applies to both Hermitian and non-Hermitian topological systems.

Numerical simulations confirm the visibility of edge states through transmission patterns.

Abstract

Particle beam scattering is a conventional technique for detecting the nature of matter. We studied the scattering problem of a cluster connected to multiple leads. We established the connection between the eigenstate of the topological scattering center and the transmission and reflection amplitudes for the resonant scattering process. We discovered that as an application, this approach enables the detection of the edge state in the band gap for both Hermitian and non-Hermitian systems and the identification of the topology of a system. We investigated two types of Su-Schrieffer-Heeger chains as examples. In addition, we proposed a dynamic scheme through an evanescently coupled-waveguide array to detect the edge state on the basis of measured transmission intensity. Numerical simulation revealed that pattern visibility can be the signature of the edge states.