Temperature dependence of fluxoid quantization in a superconducting hollow cylinder

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Abstract
Using the Ginzburg-Landau theory the magnetic response of a long hollow cylinder is calculated. Emphasis is placed on the magnetic properties as a function of temperature in a constant applied magnetic field. The only restriction is that the wall thickness is less than twice the temperature-dependent coherence length. The penetration depth is of arbitrary value as are the cylinder radius and wall thickness. The fluxoid is quantized. In the limit that the order parameter approaches zero, we obtain the quasiperiodic magnetic-field-temperature phase boundary between the normal and superconducting states. This boundary is either a second-order phase transition or a supercooling boundary. The dividing point between the two, the Landau critical point, was derived and investigated for arbitrary values of the fluxoid quantum number. The latter does not always exist for arbitrary cylinder dimensions and quantum numbers. A consequence of the appearance of a supercooling boundary is a superheating boundary which was obtained numerically from the nonlinear equations. The latter may exist, in particular for larger fluxoid quantum numbers, at a temperature beyond that of the maximum supercooling temperature. Agreement of our results with published experiments is found to be good.