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The maximal current carried by a normal–superconducting interface in the absence of magnetic field

Part of: Applications to specific types of physical systems Asymptotic theory Boundary value problems

Published online by Cambridge University Press:  27 August 2019

L. K. HART  and
Y. ALMOG Open the ORCID record for Y. ALMOG [Opens in a new window]
L. K. HART
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, LA70803, USA email: lhart31@math.gatech.edu
Y. ALMOG
Affiliation:
Department of Mathematics, Ort Braude College, Carmiel21610, Israel email: yalmog@braude.ac.il
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Abstract

Modelling a normal–superconducting interface, we consider a semi-infinite wire whose edge is adjacent to a normal magnetic metal, assuming asymptotic convergence, away from the boundary, to the purely superconducting state. We obtain that the maximal current which can be carried by the interface diminishes in the small normal conductivity limit.

Keywords

superconductivitymaximal currentnormal conductivityGinzburg-Landau

MSC classification

Primary: 82D55: Superconductors
Secondary: 34E10: Perturbations, asymptotics 34B15: Nonlinear boundary value problems
Type
Papers
Information
European Journal of Applied Mathematics , Volume 31 , Issue 3 , June 2020 , pp. 544 - 552
Copyright
© Cambridge University Press 2019

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Footnotes

†

This research was supported by NSF Grant DMS-1613471.

References

Abramowitz, M. & Stegun, I. A.Handbook of Mathematical Functions, Dover, 1972.Google Scholar
Almog, Y. (2012) The interface between the normal state and the fully superconducting state in the presence of an electric current. Commun. Contemp. Math. 14, 1250026, 27.CrossRefGoogle Scholar
Almog, Y., Berlyand, L., Golovaty, D. & Shafrir, I. (2015) Existence and stability of superconducting solutions for the Ginzburg–Landau equations in the presence of weak electric currents. J. Math. Phys. 56, 071502, 13.CrossRefGoogle Scholar
Almog, Y., Berlyand, L., Golovaty, D. & Shafrir, I. (2016) Existence of superconducting solutions for a reduced Ginzburg-Landau model in the presence of strong electric currents, SIAM J. Math. Anal. 51, 873–912. (2019).CrossRefGoogle Scholar
Berger, J. (2015) Influence of the boundary conditions on the current flow pattern along a superconducting wire. Phys. Rev. B 92, 064513.CrossRefGoogle Scholar
de Gennes, P. G. & Prost, J. (1995) The Physics of Liquid Crystals, 2nd. ed.Clarendon Press, Oxford, UK.CrossRefGoogle Scholar
Gennes, P. G. D. (1966) Superconductivity of Metals and Alloys, Westview, Boulder, CO.Google Scholar
Ivlev, B. I. & Kopnin, N. B. (1984) Electric currents and resistive states in thin superconductors. Adv. Phys. 33, 47–114.CrossRefGoogle Scholar
Ivlev, B. I., Kopnin, N. B. & Maslova, L. A. (1982) Stability of current-carrying states in narrow finite-length superconducting channels. Zh. Eksp. Teor. Fiz. 83, 1533–1545.Google Scholar
Kallush, S. & Berger, J. (2014) Qualitative modifications and new dynamic phases in the phase diagram of one-dimensional superconducting wires driven with electric currents. Phys. Rev. B 89, 214509.CrossRefGoogle Scholar
Rubinstein, J., Sternberg, P. & Kim, J. (2010) On the behavior of a superconducting wire subjected to a constant voltage difference. SIAM J. Appl. Math. 70, 1739–1760.CrossRefGoogle Scholar
Rubinstein, J., Sternberg, P. & Ma, Q. (2007) Bifurcation diagram and pattern formation of phase slip centers in superconducting wires driven with electric currents. Phys. Rev. Lett. 99, 167003.CrossRefGoogle ScholarPubMed
Rubinstein, J., Sternberg, P. & Zumbrun, K. (2010) The resistive state in a superconducting wire: bifurcation from the normal state. Arch. Ration. Mechan. Anal. 195, 117–158.CrossRefGoogle Scholar
Tinkham, M. (1996) Introduction to Superconductivity, McGraw-Hill, Mineola, NY.Google Scholar