Bifurcation to vortex solutions in superconducting films

The bifurcation from a normally conducting state to a superconducting state in a decreasing magnetic field is studied for a slab geometry. The leading eigenvalue is a double eigenvalue, leading to a rich structure of possible behaviours. A weakly-nonlinear stability analysis is performed, and the possible responses of the material are classified. Finally, the leading-order equations are solved numerically for a wide range of parameter values to determine which of these behaviours will occur in practice.