Lack of Diamagnetism and the Little-Parks Effect

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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 kappa. The analysis is based on an understanding of the underlying spectral theory for a magnetic Schrodinger 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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  • Mathematics
Original languageEnglish
Pages (from-to)191-224
JournalCommunications in Mathematical Physics
Volume337
Issue number1
Publication statusPublished - 2015
Publication categoryResearch
Peer-reviewedYes