# Lack of Diamagnetism and the Little-Parks Effect

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**Lack of Diamagnetism and the Little-Parks Effect.** / Fournais, Soren; Persson Sundqvist, Mikael.

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*Communications in Mathematical Physics*, vol. 337, no. 1, pp. 191-224. https://doi.org/10.1007/s00220-014-2267-7

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*Communications in Mathematical Physics*,

*337*(1), 191-224. https://doi.org/10.1007/s00220-014-2267-7

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*Communications in Mathematical Physics*. 2015, 337(1). 191-224. https://doi.org/10.1007/s00220-014-2267-7

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TY - JOUR

T1 - Lack of Diamagnetism and the Little-Parks Effect

AU - Fournais, Soren

AU - Persson Sundqvist, Mikael

PY - 2015

Y1 - 2015

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 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.

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 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.

U2 - 10.1007/s00220-014-2267-7

DO - 10.1007/s00220-014-2267-7

M3 - Article

VL - 337

SP - 191

EP - 224

JO - Communications in Mathematical Physics

T2 - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 1432-0916

IS - 1

ER -