Universality in low-dimensional BCS theory

Abstract

It is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature $\Xi$ and the critical temperature $T_c$ is (approximately) given by a universal constant, independent of the microscopic details of the fermionic interaction. This universality has rigorously been proven quite recently in three spatial dimensions and three different limiting regimes: weak coupling, low density, and high density. The goal of this short note is to extend the universal behavior to lower dimensions $d=1,2$ and give an exemplary proof in the weak coupling limit.

19 pages. Contribution to the proceedings of QMath15

References in corpus (4)

• Superconducting nanowire single-photon detectors: physics and applications
• Critical Temperature and Energy Gap for the BCS Equation
• The BCS Functional for General Pair Interactions
• The BCS Critical Temperature for Potentials with Negative Scattering Length

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• Bounds on $T_c$ in the Eliashberg theory of Superconductivity. I: The $\gamma$-model
• BCS Critical Temperature on Half-Spaces
• Linear Criterion for an Upper Bound on the Bardeen-Cooper-Schrieffer Critical Temperature
• Enhanced Superconductivity at a Corner for the Linear BCS Equation
• Implementing Bogoliubov Transformations Beyond the Shale-Stinespring Condition