Abstract
We study the critical temperature of a superconductive material in a weak external electric potential via a linear approximation of the BCS functional. We reproduce a similar result as in Frank et al. (Commun Math Phys 342(1):189–216, 2016, [5]) using the strategy introduced in Frank et al. (The BCS critical temperature in a weak homogeneous magnetic field, [2]), where we considered the case of an external constant magnetic field.
Dedicated to Herbert Spohn on the occasion of his seventieth birthday
© 2018 by the authors. This paper may be reproduced, in its entirety, for noncommercial purposes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Frank, R.L., Lemm, M.: Ginzburg-Landau theory with multiple order parameters: microscopic derivation and examples. Ann. H. Poincaré 17(9), 2285–2340 (2016)
Frank, R.L., Hainzl, C., Langmann, E.: The BCS critical temperature in a weak homogeneous magnetic field, to appear in J. Spect. Theory
Frank, R.L., Hainzl, C., Naboko, S., Seiringer, R.: The critical temperature for the BCS equation at weak coupling. J. Geom. Anal. 17, 559–568 (2007)
Frank, R.L., Hainzl, C., Seiringer, R., Solovej, J.P.: Microscopic derivation of Ginzburg-Landau theory. J. Am. Math. Soc. 25(3), 667–713 (2012)
Frank, R.L., Hainzl, C., Seiringer, R., Solovej, J.P.: The external field dependence of the BCS critical temperature. Commun. Math. Phys. 342(1), 189–216 (2016)
Hainzl, C., Seiringer, R.: Critical temperature and energy gap in the BCS equation. Phys. Rev. B 77, 184517 (2008)
Hainzl, C., Seiringer, R.: The Bardeen-Cooper-Schrieffer functional of superconductivity and its mathematical properties. J. Math. Phys. 57, 021101 (2016)
Hainzl, C., Hamza, E., Seiringer, R., Solovej, J.P.: The BCS functional for general pair interactions. Commun. Math. Phys. 281(2), 349–367 (2008)
Helfand, E., Werthamer, R.: Temperature and purity dependence of the superconducting critical field, Hc2. II. Phys. Rev. 147(1), 288–294 (1966)
Langmann, E.: Theory of the upper critical magnetic field without local approximation. Phys. C 159, 561 (1989)
Langmann, E.: Bc2(T) of anisotropic systems: some explicit results. Phys. B 165–166, 1061 (1990)
Langmann, E.: On the upper critical field of anisotropic superconductors. Phys. C 173, 347 (1991)
Schossmann, M., Schachinger, E.: Strong-coupling theory of the upper critical magnetic field Hc2. Phys. Rev. B 33, 6123 (1986)
Werthamer, N.R., Helfand, E., Hohenberg, P.C.: Temperature and purity dependence of the superconducting critical field, Hc2. III. Phys. Rev. 147, 295 (1966)
Acknowledgements
We thank Edwin Langmann who initiated and coauthored our previous work [2] which forms the basis of the present paper. We further thank Robert Seiringer and Jan Philip Solovej for our long-lasting collaboration on BCS theory. Further, partial support by the U.S. National Science Foundation through grant DMS-1363432 (R.L.F.) is acknowledged.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Frank, R.L., Hainzl, C. (2018). The BCS Critical Temperature in a Weak External Electric Field via a Linear Two-Body Operator. In: Cadamuro, D., Duell, M., Dybalski, W., Simonella, S. (eds) Macroscopic Limits of Quantum Systems. MaLiQS 2017. Springer Proceedings in Mathematics & Statistics, vol 270. Springer, Cham. https://doi.org/10.1007/978-3-030-01602-9_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-01602-9_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-01601-2
Online ISBN: 978-3-030-01602-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)