Classically bound and quantum quasi-bound states of an electron on a plane adjacent to a magnetic monopole

J. Martin; A. Baskerville; V. L. Campo; J. Minns; J. Pooley; S. T. Carr; C. A. Hooley; G. Möller; J. Quintanilla

doi:10.1098/rspa.2025.0072

Classically bound and quantum quasi-bound states of an electron on a plane adjacent to a magnetic monopole

J. Martin
, A. Baskerville
, V. L. Campo
, J. Minns
, J. Pooley
, S. T. Carr
, C. A. Hooley
, G. Möller
, J. Quintanilla

Research Centre for Fluid and Complex Systems

University of Kent
Federal University of São Carlos

Research output: Contribution to journal › Article › peer-review

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. 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.

Original language	English
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	481
Issue number	2326
Early online date	26 Nov 2025
DOIs	https://doi.org/10.1098/rspa.2025.0072
Publication status	E-pub ahead of print - 26 Nov 2025

Funding

J. Quintanilla acknowledges support from the EPSRC under the project ‘Unconventional superconductors: new paradigms for new materials’ (grant no. EP/P00749X/1). C. Hooley is grateful for financial support from UKRI via grant no. EP/R031924/1. This work was performed in part at Aspen Center for Physics, which is supported by National Science Foundation under grant no. PHY-2210452. G. Möller acknowledges support from the Royal Society under a University Research Fellowship (grant nos. UF120157 and URFR180004); G. Möller and J. Pooley were supported by the Royal Society Enhancement Award RGFEA180107. Acknowledgements

Funders	Funder number
Engineering and Physical Sciences Research Council	EP/P00749X/1
The Royal Society	RGFEA180107, UF120157, URFR180004
National Science Foundation	PHY-2210452
UK Research and Innovation	EP/R031924/1

Keywords

magnetic monopole
two-dimensional confinement
quasi-bound states

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10.1098/rspa.2025.0072

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Martin, J., Baskerville, A., Campo, V. L., Minns, J., Pooley, J., Carr, S. T., Hooley, C. A., Möller, G., & Quintanilla, J. (2025). Classically bound and quantum quasi-bound states of an electron on a plane adjacent to a magnetic monopole. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 481(2326). Advance online publication. https://doi.org/10.1098/rspa.2025.0072

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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. 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.",

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AU - Campo, V. L.

AU - Minns, J.

AU - Pooley, J.

AU - Carr, S. T.

AU - Hooley, C. A.

AU - Möller, G.

AU - Quintanilla, J.

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AB - 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.

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Classically bound and quantum quasi-bound states of an electron on a plane adjacent to a magnetic monopole

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