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. The threshold monopole magnetic charge required to realize a single quasi-bound state is approximately 18 Q 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, magnetic needles, image charges in magnetoelectric materials and emergent quantum excitations in Josephson junction arrays or superconducting films.