论文标题
BCS模型中的边界超导性
Boundary Superconductivity in the BCS Model
论文作者
论文摘要
我们考虑线性BCS方程，确定BCS临界温度的存在，在施加Dirichlet边界条件的边界。在与点相互作用的一维情况下，我们证明，临界温度严格大于较大的耦合，至少在弱耦合下。特别是，Cooper-Pair Wave函数位于边界附近，这种效果无法通过有效的Neumann边界条件对Ginzburg-Landau理论中经常施加的顺序参数进行建模。我们还表明，如果耦合常数要么零或无穷大，临界温度的相对变化就会消失。
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.
