Eigenvalues and Eigenfunctions of Two Coupled Normal Metal Nano-rings

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.