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Lack of Diamagnetism and the Little-Parks Effect

Fournais, Soren and Persson Sundqvist, Mikael LU (2015) In Communications in Mathematical Physics 337(1). p.191-224
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... (More)
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. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Communications in Mathematical Physics
volume
337
issue
1
pages
191 - 224
publisher
Springer
external identifiers
  • wos:000353504700009
  • scopus:84939994319
ISSN
1432-0916
DOI
10.1007/s00220-014-2267-7
language
English
LU publication?
yes
id
cf3f7236-616d-4673-9d68-52f95d2c1237 (old id 5385891)
date added to LUP
2015-05-19 10:34:43
date last changed
2017-02-09 12:08:49
@article{cf3f7236-616d-4673-9d68-52f95d2c1237,
  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       = {Fournais, Soren and Persson Sundqvist, Mikael},
  issn         = {1432-0916},
  language     = {eng},
  number       = {1},
  pages        = {191--224},
  publisher    = {Springer},
  series       = {Communications in Mathematical Physics},
  title        = {Lack of Diamagnetism and the Little-Parks Effect},
  url          = {http://dx.doi.org/10.1007/s00220-014-2267-7},
  volume       = {337},
  year         = {2015},
}