Phase transitions in thin mesoscopic superconducting disks

Phase transitions between different superconducting states and between the superconducting-normal state of mesoscopic disks are studied by solving the two Ginzburg-Landau (GL) equations self-consistently. We limit ourselves to superconducting states with a fixed angular momentum for disks thinner than the coherence length. We iind that the type of phase transition depends on the disk size, namely, both the radius and the thickness. Using an expansion over the eigenfunction of the linearized first GL equation, we develop an analytical approach that allows us to predict the type of phase transition and find the system characteristics near the phase transition point. The analytical results are in good agreement with results from our simulation obtained by using finite-difference techniques to solve the nonlinear GL equations coupled to the three-dimensional Maxwell equations. A new type of first-order phase transition between different superconducting states having the same angular momentum is predicted.