# Lack of Diamagnetism and the Little-Parks Effect

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### Bibtex

@article{cf3f7236616d46739d6852f95d2c1237,

title = "Lack of Diamagnetism and the Little-Parks Effect",

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.",

author = "Soren Fournais and {Persson Sundqvist}, Mikael",

year = "2015",

doi = "10.1007/s00220-014-2267-7",

language = "English",

volume = "337",

pages = "191--224",

journal = "Communications in Mathematical Physics",

issn = "1432-0916",

publisher = "Springer",

number = "1",

}