有角的表面超导电性
Surface Superconductivity in Presence of Corners
摘要：
我们考虑具有非光滑截面的极端II型超导导线，即，在金兹伯格-朗道理论的框架中，在边界处有一个或多个角。我们证明了存在的一个区间的值的应用领域，超导性是均匀分布沿边界的样品。更确切地说，能量不受角点的存在和Ginzburg-Landau极小化的模的主导阶沿横向方向近似恒定。界定这种表面超导制度的临界场与没有边界奇点的临界场一致。
英文摘要：
We consider an extreme type-II superconducting wire with non-smooth cross section, i.e., with one or more corners at the boundary, in the framework of the Ginzburg-Landau theory. We prove the existence of an interval of values of the applied field, where superconductivity is spread uniformly along the boundary of the sample. More precisely the energy is not affected to leading order by the presence of corners and the modulus of the Ginzburg-Landau minimizer is approximately constant along the transversal direction. The critical fields delimiting this surface superconductivity regime coincide with the ones in absence of boundary singularities.
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