Lack of Diamagnetism and the Little–Parks Effect

Søren Fournais; Mikael Persson Sundqvist

doi:10.1007/s00220-014-2267-7

Lack of Diamagnetism and the Little–Parks Effect

Søren Fournais^*, Mikael Persson Sundqvist

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Abstract

When a superconducting sample is submitted to a sufficiently strong external magnetic field, the superconductivity of the material is lost. In this paper we prove that this effect does not, in general, take place at a unique value of the external magnetic field strength. Indeed, for a sample in the shape of a narrow annulus the set of magnetic field strengths for which the sample is superconducting is not an interval. This is a rigorous justification of the Little–Parks effect. We also show that the same oscillation effect can happen for disc-shaped samples if the external magnetic field is non-uniform. In this case the oscillations can even occur repeatedly along arbitrarily large values of the Ginzburg–Landau parameter κ. The analysis is based on an understanding of the underlying spectral theory for a magnetic Schrödinger operator. It is shown that the ground state energy of such an operator is not in general a monotone function of the intensity of the field, even in the limit of strong fields.

Original language	English
Journal	Communications in Mathematical Physics
Volume	337
Issue	1
Pages (from-to)	191-224
Number of pages	36
ISSN	0010-3616
DOIs	https://doi.org/10.1007/s00220-014-2267-7
Publication status	Published - 13 Jan 2015

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10.1007/s00220-014-2267-7

Semiclassical Quantum Mechanics
Fournais, S. (PI), Madsen, P. (Participant), Mikkelsen, S. (Participant), Miqueu, J.-P. C. (Participant) & Bley, G. (Participant)
01/07/2015 → 31/12/2020
Project: Research

Cite this

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N2 - When a superconducting sample is submitted to a sufficiently strong external magnetic field, the superconductivity of the material is lost. In this paper we prove that this effect does not, in general, take place at a unique value of the external magnetic field strength. Indeed, for a sample in the shape of a narrow annulus the set of magnetic field strengths for which the sample is superconducting is not an interval. This is a rigorous justification of the Little–Parks effect. We also show that the same oscillation effect can happen for disc-shaped samples if the external magnetic field is non-uniform. In this case the oscillations can even occur repeatedly along arbitrarily large values of the Ginzburg–Landau parameter κ. The analysis is based on an understanding of the underlying spectral theory for a magnetic Schrödinger operator. It is shown that the ground state energy of such an operator is not in general a monotone function of the intensity of the field, even in the limit of strong fields.

AB - When a superconducting sample is submitted to a sufficiently strong external magnetic field, the superconductivity of the material is lost. In this paper we prove that this effect does not, in general, take place at a unique value of the external magnetic field strength. Indeed, for a sample in the shape of a narrow annulus the set of magnetic field strengths for which the sample is superconducting is not an interval. This is a rigorous justification of the Little–Parks effect. We also show that the same oscillation effect can happen for disc-shaped samples if the external magnetic field is non-uniform. In this case the oscillations can even occur repeatedly along arbitrarily large values of the Ginzburg–Landau parameter κ. The analysis is based on an understanding of the underlying spectral theory for a magnetic Schrödinger operator. It is shown that the ground state energy of such an operator is not in general a monotone function of the intensity of the field, even in the limit of strong fields.

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Lack of Diamagnetism and the Little–Parks Effect

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Semiclassical Quantum Mechanics

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