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Hainzl, Christian ORCID logoORCID: https://orcid.org/0000-0002-9772-7323; Roos, Barbara und Seiringer, Robert (2022): Boundary superconductivity in the BCS Model. In: Journal of Spectral Theory, Bd. 12, Nr. 4: S. 1507-1540

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Abstract

We consider the linear BCS equation, determining the BCS critical temperature, in the presence of a boundary, where Dirichlet boundary conditions are imposed. In the one-dimen-sional case with point interactions, we prove that the critical temperature is strictly larger than the bulk value, at least at weak coupling. In particular, the Cooper-pair wave function localizes near the boundary, an effect that cannot be modeled by effective Neumann boundary conditions on the order parameter as often imposed in Ginzburg-Landau theory. We also show that the relative shift in critical temperature vanishes if the coupling constant either goes to zero or to infinity.

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