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Chinese Journal of Physics

The Aharonov-Bohm Effect and Its Applications to Superconducting Flux Line Observation

Akira Tonomura

Published Dec 1, 1992• 0 citations
OpenAlex

Abstract

The Aharonov-Bohm effect is experimentally confirmed to exist under ideal conditions where there is no overlap between an incident electron wave and a confined magnetic field. The experiment not only establishes the physical reality of gauge fields but also opens up a new way, based on the principle behind this effect, to observe microscopic flux lines.

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This article describes the Aharonov-Bohm (AB) effect of electron waves travelling in free space and its application to the observation of gauge fields (vector potentials). The AB effect is inconceivable in classical physics since an observable effect is produced on electrons passing through field-free spaces. Electrons can be affected only by Lorentz forces due to electromagnetic fields. The situation is different in quantum mechanics, where electrons show wave properties: the concept of force is no longer relevant, so electric field E and magnetic field B, defined as forces acting on a unit charge, take on secondary meanings. “Phase shifts” come into play, and the primary physical entities become neither E nor B but electrostatic potential V and vector potential A. These potentials interact with electron waves and shift their phases.

Asia Pacific Physics Newsletter•Jan 1, 2013•2 citations

ELECTRON HOLOGRAPHY AND AHARONOV-BOHM EFFECT

Akira Tonomura

The Aharonov-Bohm (AB) effect was tested under conditions where an electron wave and a magnetic field did not overlap: the Meissner effect of the superconductor shielding a toroidal ferromagnet eliminated the leakage field. Using the newly-developed technique of electron holography, conclusive evidence for the AB effect was obtained by detecting a relative phase shift of π between the two electron waves passing through the hole and outside the toroid. The detected phase shift value of exactly π comes from the quantization of the magnetic flux within the superconductor. This quantization assures the complete shielding of the magnetic field.

International Journal of Modern Physics B•Apr 1, 1989•3 citations
The Aharonov-Bohm effect is experimentally confirmed to exist under ideal conditions where there is no overlap between an incident electron wave and a confined magnetic field. The experiment not only establishes the physical reality of gauge fields but also opens up a new way, based on the principle behind this effect, to observe microscopic flux lines.
Electron interference phenomena are now easily observable with the advent of bright and yet coherent field-emission electron beams. The interaction of electron waves with electromagnetic fields is essentially described by the Aharonov–Bohm (AB) effect. However, the AB effect has long been disputed due to a feature that cannot be understood in terms of classical electrodynamics. This paper describes the experiments that confirmed its existence and discusses its expanding applications to the observation of electromagnetic fields in the microscopic region.
This technical note gives a self-contained exposition of the Aharonov–Bohm effect, aimed at advanced undergraduate students. Starting from the role of electromagnetic potentials in classical electrodynamics, it introduces gauge freedom, the quantum Hamiltonian with minimal coupling, and the gauge covariance of the Schrödinger equation. It then derives the Aharonov–Bohm phase for both the time-dependent scalar configuration and the magnetic configuration, showing how a charged particle acquires an observable phase shift while travelling only through regions where the electromagnetic field vanishes. The final part reviews the experimental evidence, from the early electron-interference experiments of Chambers and of Möllenstedt and Bayh to the 1986 toroidal-magnet experiment of Tonomura and collaborators. In that experiment, superconducting shielding confined the magnetic flux completely and closed the leakage-field loophole, while flux quantization produced the characteristic half-fringe shift. The note is expository and pedagogical: it does not present original research results and has not been peer reviewed. Originally developed from study notes prepared for the PHYS02 scientific talk at Lady Margaret Hall, Oxford, in July 2026; an earlier version of the notes has been publicly available on GitHub since August 2026. Corrections and comments are more than welcome at giancarminesparso@gmail.com.
The electron holography technique was employed to make a crucial test of the existence of the Aharonov-Bohm (AB) effect. The relative phase shift was measured between two electron waves passing through spaces inside and outside a tiny toroidal ferromagnet, covered completely with a superconductor layer and a Cu layer. Below the transition temperature the relative phase shift was measured to be 0 or \ensuremath{\pi} due to the magnetic-flux quantization in units of h/2e. The results directly demonstrated the existence of the AB effect even when the magnetic field was confined by the surrounding superconductor due to the Meissner effect and an electron beam was prevented from penetrating the magnet.
This article describes the Aharonov-Bohm (AB) effect of electron waves travelling in free space and its application to the observation of gauge fields (vector potentials). The AB effect is inconceivable in classical physics since an observable effect is produced on electrons passing through field-free spaces. Electrons can be affected only by Lorentz forces due to electromagnetic fields. The situation is different in quantum mechanics, where electrons show wave properties: the concept of force is no longer relevant, so electric field E and magnetic field B, defined as forces acting on a unit charge, take on secondary meanings. “Phase shifts” come into play, and the primary physical entities become neither E nor B but electrostatic potential V and vector potential A. These potentials interact with electron waves and shift their phases.
The Aharonov-Bohm (AB) effect was tested under conditions where an electron wave and a magnetic field did not overlap: the Meissner effect of the superconductor shielding a toroidal ferromagnet eliminated the leakage field. Using the newly-developed technique of electron holography, conclusive evidence for the AB effect was obtained by detecting a relative phase shift of π between the two electron waves passing through the hole and outside the toroid. The detected phase shift value of exactly π comes from the quantization of the magnetic flux within the superconductor. This quantization assures the complete shielding of the magnetic field.