Phase transition into the superconducting mixed state and the de Haas-van Alphen effect
Abstract The Landau expansion for the free energy of the superconducting mixed state near the upper critical field in powers of the sauare modulus of the order parameter averaged over an Abrikosov lattice is derived. The analytical calculations have been carried out in the framework of the Gor'kov formalism for a 3-dimensional isotropic BCS model beyond the limits of the quasiclassical approximation, that is, with Landau auantization of the auasiparticle energy levels taken into consideration. The derivation is performed at Iow temperature for finite but high enough crystal purity. The effect of Pauli paramagnetic terms is taken into account. The quantum oscillations of the critical temperature, the order parameter's amplitude and the magnetization (de Haas-van Alphen effect) in the mixed state are found. The limitation for the validity of a mean field approach due to critical fluctuations (Ginzburg criterion) for the phase transition under consideration is established.
Large-order behavior of the perturbation series for superconductors near Hc2.
The perturbation series for superconductors near {ital H}{sub {ital c}2} are studied in the two- and three-dimensional Ginzburg-Landau model. The large-order behavior is discussed first on a theoretical basis by an instanton method of Lipatov type. The results are compared with an eleventh-order calculation in two dimensions and a sixth-order one in three dimensions, and show good agreement with the theoretical prediction. The conjectures based on an Abrikosov lattice configuration seem to be ruled out.
de Haas-van Alphen oscillations in a superconducting state at high magnetic fields.
Low-temperature quantum oscillations of the dHvA amplitude are shown to persist far below the upper critical field of a strongly type-II superconductor, due to the gapless nature of the BCS quasiparticle spectrum in high fields. The dHvA amplitude in the superconducting state is smaller than its normal state countpart by factor ~[max(T,Gamma]/delta]**2, where Gamma is the damping. This factor reflects the presence of a small gapless portion of the fermi surface, surrounded by regions where the BCS gap is large. The agreement with recent experimental data on V3Si is very good.