BCS Critical Temperature on Half-Spaces

Abstract

We study the BCS critical temperature on half-spaces in dimensions $d=1,2,3$ with Dirichlet or Neumann boundary conditions. We prove that the critical temperature on a half-space is strictly higher than on ${\mathbb{R}}^d$, at least at weak coupling in $d=1,2$ and weak coupling and small chemical potential in $d=3$. Furthermore, we show that the relative shift in critical temperature vanishes in the weak coupling limit.

64 pages, 5 figures; published version

References in corpus (5)

• Critical Temperature and Energy Gap for the BCS Equation
• The BCS Functional for General Pair Interactions
• Boundary effects in two-band superconductors
• Universality in low-dimensional BCS theory
• Linear Criterion for an Upper Bound on the Bardeen-Cooper-Schrieffer Critical Temperature

Cited by in corpus (2)

• Ginzburg-Landau Theory for Confined Thin-Film Superconductors
• Designing edge currents using mesoscopic patterning in chiral d-wave superconductors