Thermodynamics of the re-entrant regime of type II two-dimensional superconductivity in a strong transverse magnetic field

The thermodynamics (including energy gap and critical temperatureT _c ) of a two-dimensional type II BCS superconductor subjected to a strong transverse magnetic fieldH in the re-entrant regime is studied. There are qualitative differences with the re-entrant 3D case; in particularT _c grows unboundedly likeB/lnB asB (filling factor 1) for fixedN. The thermodynamics atT=0 is completely described by the evaluation of the magnetic Gibbs free energy as a function of andH. A first order magnetic phase transition (failure of H/ B>0 for around each lowlying Landau level) found for the normal phase for unbroadened Landau levels, is washed out in the superconducting phase.