Classically Bound and Quantum Quasi-Bound States of an Electron on a Plane Adjacent to a Magnetic Monopole

TL;DR

This paper investigates the existence of bound and quasi-bound electron states near a magnetic monopole in a two-dimensional setting, revealing potential for high magnetic charges in experimental analogues.

Contribution

It introduces the concept of bound and quasi-bound states of an electron on a plane near a magnetic monopole, including lifetime calculations and experimental feasibility analysis.

Findings

Bound states exist classically in 2D near monopoles.

Quantum quasi-bound states have finite lifetimes.

Magnetic charge of about 18 times Dirac's charge is needed for a single quasi-bound state.

Abstract

In three-dimensional space an electron moving in the field of a magnetic monopole has no bound states. In this paper we explore the physics when the electron is restricted to a two-dimensional plane adjacent to a magnetic monopole. We find bound states in the classical version of the problem and quasi-bound states in the quantum one, in addition to a continuum of scattering states. We calculate the lifetimes of the quasi-bound states using several complementary approximate methods, which agree well in the cases where the lifetimes are relatively short. The threshold monopole magnetic charge required to realise a single quasi-bound state is approximately $18Q_D$, where $Q_D$ is the magnetic charge of a Dirac monopole. We examine the feasibility of achieving this magnetic charge in currently available monopole analogues: spin ice, artificial spin ice, and magnetic needles.