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.

arXiv comment19 pages. Contribution to the proceedings of QMath15

References in corpus (14)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• 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 functional of superconductivity and its mathematical properties
• The BCS Critical Temperature for Potentials with Negative Scattering Length
• Multi-component Ginzburg-Landau theory: microscopic derivation and examples
• Low Density Limit of BCS Theory and Bose-Einstein Condensation of Fermion Pairs
• Ubiquity of superconducting domes in BCS theory with finite-range potentials
• Weak coupling limit for Schrödinger-type operators with degenerate kinetic energy for a large class of potentials
• The BCS Energy Gap at High Density
• The BCS Critical Temperature at High Density
• The BCS Energy Gap at Low Density
• Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in a Weak Homogeneous Magnetic Field

Cited by in corpus (5)

• 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