The external field dependence of the BCS critical temperature

Abstract

We consider the Bardeen-Cooper-Schrieffer free energy functional for particles interacting via a two-body potential on a microscopic scale and in the presence of weak external fields varying on a macroscopic scale. We study the influence of the external fields on the critical temperature. We show that in the limit where the ratio between the microscopic and macroscopic scale tends to zero, the next to leading order of the critical temperature is determined by the lowest eigenvalue of the linearization of the Ginzburg-Landau equation.

28 pages

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
• The BCS Critical Temperature for Potentials with Negative Scattering Length

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• Persistence of translational symmetry in the BCS model with radial pair interaction
• General pairing mechanisms in the BCS-theory of superconductivity
• Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in a Weak Homogeneous Magnetic Field
• An operator-theoretical study of the specific heat and the critical magnetic field in the BCS-Bogoliubov model of superconductivity
• Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in General External Fields
• A lower bound for the BCS functional with boundary conditions at infinity
• Another operator-theoretical proof for the second-order phase transition in the BCS-Bogoliubov model of superconductivity
• Linear Criterion for an Upper Bound on the Bardeen-Cooper-Schrieffer Critical Temperature
• An operator-theoretical study on the BCS-Bogoliubov model of superconductivity near absolute zero temperature
• Differential Equations of Quantum Mechanics