Bound states in the continuum in open Aharonov-Bohm rings

TL;DR

This paper investigates bound states in the continuum (BIC) within open Aharonov-Bohm rings, showing their orthogonality to open channels and conditions for their existence at specific energies and magnetic flux values.

Contribution

It provides an exact analysis of BICs in open Aharonov-Bohm rings using effective Hamiltonian formalism, highlighting their orthogonality and dependence on system parameters.

Findings

BICs are orthogonal to open channels and can be superposed in transport solutions.

BICs occur at discrete energies and magnetic flux values.

Existence of BICs depends on the system's configuration and parameters.

Abstract

Using formalism of effective Hamiltonian we consider bound states in continuum (BIC). They are those eigen states of non-hermitian effective Hamiltonian which have real eigen values. It is shown that BICs are orthogonal to open channels of the leads, i.e. disconnected from the continuum. As a result BICs can be superposed to transport solution with arbitrary coefficient and exist in propagation band. The one-dimensional Aharonov-Bohm rings that are opened by attaching single-channel leads to them allow exact consideration of BICs. BICs occur at discrete values of energy and magnetic flux however it's realization strongly depend on a way to the BIC's point.