Temperature dependence of the superconducting giant-vortex state. Theory and experiment

Abstract

When a type-I superconductor with a surface nucleation field $H_{c3\mathrm{}}\mathrm{}\left(T\right)>H_c\mathrm{}\left(T\right)\mathrm{}$ (thermodynamic critical field) is thermally cycled in an axially applied magnetic field $H_0$ between the temperatures $T\left(H_{c3\mathrm{}}\right)$ and about $T\left(H_c\right)$, experiments show that the magnetization changes reversibly. The latter is diamagnetic near $T\left(H_{c3\mathrm{}}\right)$ but can be paramagnetic just above $T\left(H_c\right)$. This behavior is explained by assuming that the fluxoid quantum number $b$ is fixed at the transition from the normal to the superconducting state and retained at lower temperatures. The value of $b$ is determined almost entirely by the flux at the transition which is enclosed by a contour located at a distance $\frac{\xi }{1.7}$ from the surface inside the cylinder ($\xi$ is the coherence length). The temperature variation of the order parameter $f$ at the surface of the cylinder, the magnetization $m$, and the temperature at which $m=0\mathrm{}$ for $f\ne 0$ are calculated for $R\gg \xi$. Conservation of the fluxoid quantum number, while $T$ is varied causes the two opposing surface currents to become imbalanced. This is the source of the observed para- and diamagnetism.