Perturbation theory of superconducting micronetworks: Second-order and self-induction effects

J. I. Castro; A. López

doi:10.1103/PhysRevB.46.1075

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Perturbation theory of superconducting micronetworks: Second-order and self-induction effects

J. I. Castro, A. López

DOI 10.1103/PhysRevB.46.1075 · Physical Review B

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Abstract

The perturbation method to treat the nonlinear Ginzburg-Landau equations for micronetworks previously derived is extended to higher orders in the perturbation parameters, the temperature ΔT and magnetic field ΔH measured from the phase boundary. In this paper these two parameters are treated independently and the perturbation equations to all orders are analyzed. The theory allows for consideration of self-inductive effects. The importance of these for the interpretation of experimental results in micronetworks of type-I and type-II materials is pointed out. The Landau critical points have been discussed. Expressions for the relevant thermodynamic quantities are obtained. In particular, it is shown that the phase boundary satisfies the Ehrenfest-Keesom relations for second-order transitions. The theory has been explicitly worked out for simple geometries and compared with exact results, which have been obtained numerically. The lines separating different modes have been evaluated to second order for these cases.