Meissner effect, diamagnetism, and classical physics—a review

Essén, Hanno; Fiolhais, Miguel C. N.

doi:doi:10.1119/1.3662027

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American Journal of Physics -- February 2012 -- Volume 80, Issue 2, pp. 164

Meissner effect, diamagnetism, and classical physics—a review

Hanno Essén¹ and Miguel C. N. Fiolhais²

¹Department of Mechanics, Royal Institute of Technology (KTH), Stockholm SE-100 44, Sweden
²LIP-Coimbra, Department of Physics, University of Coimbra, Coimbra 3004-516, Portugal

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Abstract

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We review the literature on what classical physics says about the Meissner effect and the London equations. We discuss the relevance of the Bohr-van Leeuwen theorem for the perfect diamagnetism of superconductors and conclude that the theorem is based on invalid assumptions. We also point out results in the literature that show how magnetic flux expulsion from a sample cooled to superconductivity can be understood as an approach to the magnetostatic energy minimum. These results have been published several times but many textbooks on magnetism still claim that there is no classical diamagnetism, and virtually all books on superconductivity repeat Meissner’s 1933 statement that flux expulsion has no classical explanation.

Article Outline

INTRODUCTION
THE BOHR-VAN LEEUWEN THEOREM AND CLASSICAL DIAMAGNETISM
1. The inadequacy of the basic assumptions
2. What about Larmor’s theorem?
3. The Shanghai experiment—measuring a diamagnetic current?
ON THE ALLEGED INCONSISTENCY OF MAGNETIC FLUX EXPULSION WITH CLASSICAL PHYSICS
1. Lippmann’s theorem
2. Lippmann’s theorem and superconductors
3. Frozen-in field lines
4. Magnetic field lines in superconductors
5. A classical derivation of the London equations
6. de Gennes’ derivation of flux expulsion
7. A purely classical derivation from magnetostatics
CONCLUSIONS