Lack of Diamagnetism and the Little-Parks Effect
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/5385891
- author
- Fournais, Soren and Persson Sundqvist, Mikael LU
- organization
- publishing date
- 2015
- 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
- 2016-04-01 10:08:00
- date last changed
- 2022-04-27 18:53:17
@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}},
doi = {{10.1007/s00220-014-2267-7}},
volume = {{337}},
year = {{2015}},
}