Lack of Diamagnetism and the LittleParks Effect
(2015) In Communications in Mathematical Physics 337(1). p.191224 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 LittleParks effect. We also show that the same oscillation effect can happen for discshaped samples if the external magnetic field is nonuniform. In this case the oscillations can even occur repeatedly along arbitrarily large values of the GinzburgLandau 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 LittleParks effect. We also show that the same oscillation effect can happen for discshaped samples if the external magnetic field is nonuniform. In this case the oscillations can even occur repeatedly along arbitrarily large values of the GinzburgLandau 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:
http://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
 14320916
 DOI
 10.1007/s0022001422677
 language
 English
 LU publication?
 yes
 id
 cf3f7236616d46739d6852f95d2c1237 (old id 5385891)
 date added to LUP
 20150519 10:34:43
 date last changed
 20180529 12:29:56
@article{cf3f7236616d46739d6852f95d2c1237, 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 LittleParks effect. We also show that the same oscillation effect can happen for discshaped samples if the external magnetic field is nonuniform. In this case the oscillations can even occur repeatedly along arbitrarily large values of the GinzburgLandau 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 = {14320916}, language = {eng}, number = {1}, pages = {191224}, publisher = {Springer}, series = {Communications in Mathematical Physics}, title = {Lack of Diamagnetism and the LittleParks Effect}, url = {http://dx.doi.org/10.1007/s0022001422677}, volume = {337}, year = {2015}, }