Ginzburg-Landau Theory of Surface Superconductivity and Magnetic Hysteresis

The magnetization properties of a long superconducting cylinder with an ideal surface and a radius much larger than the low-field penetration depth are discussed on the basis of numerical solutions to the one-dimensional Ginzburg-Landau equations for a half-space. The current-carrying properties of the complete set of nodeless surface solutions and Meissner solutions are discussed in detail, and a separate numerical investigation of infinitesimal solutions is included. A stability criterion is derived, and infinitesimal solutions are shown to be unstable below $H_{c3\mathrm{}}$. Finally these results are used for determining critical currents and magnetization curves. It is shown that there is a new kind of superheating and supercooling due to the shielding properties of the surface sheath.