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Microscopic derivation of Ginzburg-Landau theory and the BCS critical temperature shift in a weak homogeneous magnetic field

Andreas Deuchert, Christian Hainzl and Marcel Oliver Maier
Vol. 4 (2023), No. 1, 1–89
DOI: 10.2140/pmp.2023.4.1
Abstract

Starting from the Bardeen–Cooper–Schrieffer (BCS) free energy functional, we derive the Ginzburg–Landau functional in the presence of a weak homogeneous magnetic field. We also provide an asymptotic formula for the BCS critical temperature as a function of the magnetic field. This extends the previous works of Frank, Hainzl, Seiringer and Solovej (2012; 2016) to the case of external magnetic fields with nonvanishing magnetic flux through the unit cell.

Mathematical Subject Classification
Primary: 35A15, 35Q56, 82D50, 82D55
Milestones
Received: 18 August 2021
Revised: 7 July 2022
Accepted: 24 October 2022
Published: 29 March 2023
Authors
Andreas Deuchert
Institute of Mathematics
University of Zurich
Zurich
Switzerland
Christian Hainzl
Mathematisches Institut der Universität München
München
Germany
Marcel Oliver Maier
Mathematisches Institut der Universität München
München
Germany
© 2023 MSP (Mathematical Sciences Publishers).