Boundary Superconductivity in the BCS Model

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-dimensional 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.

22 pages, 1 figure; final version to appear in Journal of Spectral Theory

References in corpus (4)

• Critical Temperature and Energy Gap for the BCS Equation
• Boundary effects in two-band superconductors
• Elevated critical temperature at BCS superconductor-band insulator interfaces
• Two-Particle Bound States at Interfaces and Corners

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• Linear Criterion for an Upper Bound on the Bardeen-Cooper-Schrieffer Critical Temperature
• Enhanced Superconductivity at a Corner for the Linear BCS Equation
• Designing edge currents using mesoscopic patterning in chiral d-wave superconductors
• Superconducting order parameter in aperiodic binary systems