Phase transitions in the mesoscopic superconducting square

摘要

We solve the Ginzburg-Landau equation (GLE) for the mesoscopic thin film ofthe square shape in the magnetic field. In the limit of Ginzburg-Landauparameter $\kappa \to \infty$ we find a series of first and second order phasetransitions as temperature and/or magnetic field changes. First order phasetransitions between giant flux states can be described with a simplevariational procedure. We discuss the similarity with rotating liquid $He^4$and derive a simple formula for $H_{c1}$. We identify order parameters based onsymmetry arguments and we propose Landau functional describing the second orderphase transition.