Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in a Weak Homogeneous Magnetic Field

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 arXiv:1102.4001 and arXiv:1410.2352 of Frank, Hainzl, Seiringer and Solovej to the case of external magnetic fields with non-vanishing magnetic flux through the unit cell.

91 pages, 1 figure

References in corpus (4)

• Critical Temperature and Energy Gap for the BCS Equation
• The BCS Functional for General Pair Interactions
• A Nonlinear Model for Relativistic Electrons at Positive Temperature
• Energy Cost to Make a Hole in the Fermi Sea

Cited by in corpus (4)

• Universality in low-dimensional BCS theory
• Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in General External Fields
• Linear Criterion for an Upper Bound on the Bardeen-Cooper-Schrieffer Critical Temperature
• Enhanced Superconductivity at a Corner for the Linear BCS Equation