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

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.

💡 Research Summary

The paper investigates the dynamics of an electron confined to a two‑dimensional plane that lies a distance D above a magnetic monopole. While it is well‑known that in three dimensions an electron moving in the field of a monopole has no bound states, the authors ask whether restricting the motion to a plane can generate bound or quasi‑bound states.

Model and Classical Analysis
The electron (effective mass m* and charge qe = −|qe|) experiences only the component of the monopole field perpendicular to the plane. In Coulomb gauge the vector potential is purely azimuthal,
Aφ(r)=μ0Qm/(4πr)