Enhanced Superconductivity at a Corner for the Linear BCS Equation

Abstract

We consider the critical temperature for superconductivity, defined via the linear BCS equation. We prove that at weak coupling the critical temperature for a sample confined to a quadrant in two dimensions is strictly larger than the one for a half-space, which in turn is strictly larger than the one for ${\mathbb{R}}^2$. Furthermore, we prove that the relative difference of the critical temperatures vanishes in the weak coupling limit.

36 pages, 1 figure; published version

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• The BCS Functional for General Pair Interactions
• Boundary effects in two-band superconductors
• 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
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Cited by in corpus (1)

• Designing edge currents using mesoscopic patterning in chiral d-wave superconductors