Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in General External Fields

Abstract

We consider the Bardeen-Cooper-Schrieffer (BCS) free energy functional with weak and macroscopic external electric and magnetic fields and derive the Ginzburg-Landau functional. We also provide an asymptotic formula for the BCS critical temperature as a function of the external fields. This extends our previous results in arXiv:2105.05623 for the constant magnetic field to general magnetic fields with a nonzero magnetic flux through the unit cell.

82 pages, 1 figure. arXiv admin note: text overlap with arXiv:2105.05623

References in corpus (5)

• Critical Temperature and Energy Gap for the BCS Equation
• The BCS Functional for General Pair Interactions
• Energy Cost to Make a Hole in the Fermi Sea
• Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in a Weak Homogeneous Magnetic Field
• Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in General External Fields

Cited by in corpus (3)

• 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