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The breakdown of superconductivity due to strong fields for the Ginzburg-Landau model. (English) Zbl 1094.82021

Summary: We study the behavior of a superconducting material subjected to a constant applied magnetic field, \(\mathbf H_a=h\mathbf e\) with \(| \mathbf e| =1\), using the Ginzburg-Landau theory. We analytically show the existence of a critical field \(\bar h,\) for which, when \(h>\bar h,\) the normal states are the only solutions to the Ginzburg-Landau equations. We estimate \(\bar h\). As \(\kappa\downarrow 0\) we derive \(\bar h=O(1)\), while as \(\kappa\to\infty\) we obtain \(\bar h=O(\kappa)\).

MSC:

82D55 Statistical mechanics of superconductors
35Q55 NLS equations (nonlinear Schrödinger equations)
35A15 Variational methods applied to PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
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