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.
Categories: math-ph cond-mat.supr-con math.MP