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.