paper

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

arXiv:2501.04406 · doi:10.1098/rspa.2025.0072

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 , where 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.

arXiv comment28 pages; typos corrected including an important correction to Figure 15; author accepted manuscript

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