Flux Rule, U(1) Instanton, and Superconductivity

Journal of Superconductivity and Novel Magnetism volume 30, pages3345–3349(2017)Cite this article

Abstract

We examine some consequences of the duality that a U(1) phase factor added on a wave function describes a whole system motion and also plays the role of a U(1) gauge potential. First, we show that the duality solves a long-standing puzzling problem that the ‘flux rule’ (the Faraday’s induction formula) and the Lorentz force calculation for an emf emerging in an electron system moving in a magnetic field give the same result (Feynman et al. 1963). Next, we examine a U(1) phase factor induced on the wave function for an electron system due to the single-valuedness requirement of the wave function with respect to the electron coordinates, and its consequential appearance of a U(1) instanton. This instanton explains the Meissner effect, supercurrent generation, flux quantization in the units of \({{h} \over {2e}}\), and the voltage quantization in the units of \({{hf} \over {2e}}\) across the Josephson junction in the presence of a radiation field with frequency f. In the experiment, a radiation field must be present to have a finite voltage across the Josephson junction; but a clear explanation for it has been lacking. The present work provides an explanation for it, and also explains the high precision of the quantized voltage as due to a topological effect.

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Acknowledgments

Part of the present work was conducted during the author’s sabbatical stay at Lorentz Institute for theoretical physics, Leiden University, the Netherlands. He thanks the members of the institute for their hospitality. This work was partly supported by a grant from Delta ITP funds.

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  1. Center for Computational Sciences, University of Tsukuba, Tsukuba, Ibaraki, 305-8577, Japan

    Hiroyasu Koizumi

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  1. Hiroyasu Koizumi
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Correspondence to Hiroyasu Koizumi.

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Koizumi, H. Flux Rule, U(1) Instanton, and Superconductivity. J Supercond Nov Magn 30, 3345–3349 (2017). https://doi.org/10.1007/s10948-017-4302-3

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Keywords

  • Flux rule
  • U(1) instanton