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The breakdown of superconductivity in the presence of magnetic steps

Assaad, Wafaa LU (2021) In Communications in Contemporary Mathematics 23(2).
Abstract

Many earlier works were devoted to the study of the breakdown of superconductivity in type-II superconducting bounded planar domains, submitted to smooth magnetic fields. In the present contribution, we consider a new situation where the applied magnetic field is piecewise-constant, and the discontinuity jump occurs along a smooth curve meeting the boundary transversely. To handle this situation, we perform a detailed spectral analysis of a new effective model. Consequently, we establish the monotonicity of the transition from a superconducting to a normal state. Moreover, we determine the location of superconductivity in the sample just before it disappears completely. Interestingly, the study shows similarities with the case of corner... (More)

Many earlier works were devoted to the study of the breakdown of superconductivity in type-II superconducting bounded planar domains, submitted to smooth magnetic fields. In the present contribution, we consider a new situation where the applied magnetic field is piecewise-constant, and the discontinuity jump occurs along a smooth curve meeting the boundary transversely. To handle this situation, we perform a detailed spectral analysis of a new effective model. Consequently, we establish the monotonicity of the transition from a superconducting to a normal state. Moreover, we determine the location of superconductivity in the sample just before it disappears completely. Interestingly, the study shows similarities with the case of corner domains subjected to constant fields.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
diamagnetic inequality, Ginzburg-Landau equations, magnetic Laplacian, step magnetic fields
in
Communications in Contemporary Mathematics
volume
23
issue
2
article number
2050005
publisher
World Scientific Publishing
external identifiers
  • scopus:85082045802
ISSN
0219-1997
DOI
10.1142/S0219199720500054
language
English
LU publication?
yes
id
dcd6709c-6a6c-48d3-999c-e202a987e1b6
date added to LUP
2020-04-08 09:41:12
date last changed
2021-04-16 12:37:51
@article{dcd6709c-6a6c-48d3-999c-e202a987e1b6,
  abstract     = {<p>Many earlier works were devoted to the study of the breakdown of superconductivity in type-II superconducting bounded planar domains, submitted to smooth magnetic fields. In the present contribution, we consider a new situation where the applied magnetic field is piecewise-constant, and the discontinuity jump occurs along a smooth curve meeting the boundary transversely. To handle this situation, we perform a detailed spectral analysis of a new effective model. Consequently, we establish the monotonicity of the transition from a superconducting to a normal state. Moreover, we determine the location of superconductivity in the sample just before it disappears completely. Interestingly, the study shows similarities with the case of corner domains subjected to constant fields.</p>},
  author       = {Assaad, Wafaa},
  issn         = {0219-1997},
  language     = {eng},
  number       = {2},
  publisher    = {World Scientific Publishing},
  series       = {Communications in Contemporary Mathematics},
  title        = {The breakdown of superconductivity in the presence of magnetic steps},
  url          = {http://dx.doi.org/10.1142/S0219199720500054},
  doi          = {10.1142/S0219199720500054},
  volume       = {23},
  year         = {2021},
}