Mesoscopic superconductors in the London limit: Equilibrium properties and metastability

We present a study of the behavior of metastable vortex states in mesoscopic superconductors. Our analysis relies on the London limit within which it is possible to derive closed analytical expressions for the magnetic field and the Gibbs free energy. We consider in particular the situation where the vortices are symmetrically distributed along a closed ring. There, we obtain expressions for the confining Bean-Livingston barrier and for the magnetization which turns out to be paramagnetic away from thermodynamic equilibrium. At low temperature, the barrier is high enough for this regime to be observable. We propose also a local description of both thermodynamic and metastable states based on elementary topological considerations; we find structural phase transitions of vortex patterns between these metastable states and we calculate the corresponding critical fields.