BCS模型中的边界超导性
Boundary Superconductivity in the BCS Model
AI总结：
本文研究了施加Dirichlet边界条件下的线性BCS方程与临界温度，证明一维点相互作用中弱耦合时临界温度严格大于体相值且Cooper对波函数在边界局域化，该效应无法被Ginzburg-Landau理论的有效Neumann边界条件建模，且耦合常数趋于零或无穷大时相对偏移消失。
摘要：
我们考虑在存在边界且施加Dirichlet边界条件的情况下，决定BCS临界温度的线性BCS方程。在具有点相互作用的一维情形中，我们证明了至少在弱耦合下，临界温度严格大于体相值。特别地，Cooper对波函数在边界附近局域化，这一效应无法用Ginzburg-Landau理论中通常对序参量施加的有效Neumann边界条件来建模。我们还证明了，如果耦合常数趋于零或趋于无穷大，临界温度的相对偏移则消失。
英文摘要：
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.
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