Eigenvalues and Eigenfunctions of Two Coupled Normal Metal Nano-rings

TL;DR

This paper develops a comprehensive method to analyze the eigenvalues and eigenfunctions of two coupled normal metal nano-rings, revealing the potential for localized states beyond prior expectations.

Contribution

It introduces a general scheme for solving 1D lattice systems, specifically applied to coupled nano-rings, uncovering new localized states.

Findings

Existence of localized eigenstates in coupled nano-rings

Method allows complete determination of eigenvalues and eigenfunctions

Potential implications for nano-electronic device design

Abstract

A general scheme is developed to deal with 1D lattice systems that could be topologically complicated. It is aimed to give a complete study of two coupled normal metal rings. Our method starts with an investigation of the local expressions of the eigenfunctions. By connecting different parts of the system, all the eigenvalues and eigenfunctions can be obtained. It is found that there is a possibility for the existence of localized states, which is beyond previous expectations.