Superconductivity near the normal state in a half-plane under the action of a perpendicular electric current and an induced magnetic field

Almog, Yaniv; Helffer, Bernard; Pan, Xing-Bin

doi:10.1090/S0002-9947-2012-05572-3

Superconductivity near the normal state in a half-plane under the action of a perpendicular electric current and an induced magnetic field
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by Yaniv Almog, Bernard Helffer and Xing-Bin Pan PDF

Trans. Amer. Math. Soc. 365 (2013), 1183-1217 Request permission

Abstract:

We consider the linearization of the time-dependent Ginzburg-Landau system near the normal state. We assume that a constant magnetic field and an electric current are applied through the sample, which captures half of the plane, inducing thereby a linearly varying magnetic field. In the limit of small normal conductivity we prove that if the electric current is lower than some critical value, the normal state loses its stability. For currents stronger than this critical value, the normal state is stable. To obtain this stability result we analyze both the spectrum and the pseudo-spectrum of the linearized operator. The critical current tends, in this small conductivity limit, to another critical current which had been obtained for a reduced model which neglects magnetic field effects.

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