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.
Nucleation of Superconductivity in Low-Dimensional Systems Under Magnetic Fields
This chapter presents a survey of the current state of art of the theory of the upper critical field in low-dimensional superconducting materials. Starting from the Ginzburg-Landau equation in the vicinity of the critical temperature we derive a new analytical expression for the angular and temperature dependence of the critical field in layered superconducting materials. This formula is shown to reproduce as limiting cases the well known results of Tinkham for an isolated film of finite thickness and of Lawrence-Doniach for the stacked array of films of zero thickness with its particular anisotropic Ginzburg-Landau limit. The well known theoretical statements of A.Lebed’ about a low temperature divergence of the upper critical field parallel to the conducting layers in the layered superconductors and the reentrance of the superconductivity in ultra-high magnetic fields are reinvestigated taking into account the scattering of quasiparticles by impurities. The upper limit of the superconductor purity yielding to a finite value of the upper critical field is established. The problem of the low temperature divergence of the upper critical field in bulk materials in the quantized magnetic field is discussed. The high field behavior of the critical temperature as a function of the magnetic field for a finite but high enough crystal purity is derived.
Non-trivial magnetic order in URu2Si2?
We have searched for the hidden multispin order parameters that have been proposed to explain the weak ordered moment observed in the heavy-fermion superconductor URu2Si2. Since the exotic spin order is predicted to cause broken-symmetry Bragg peaks that develop rapidly with applied magnetic field, we have measured their strength in fields up to 8 T, for which a large easily observable moment is predicted. The Bragg neutron scattering is found to decrease rather than increase when a field is applied along the easy tetragonal c-axis, while there is no change for a field at right angles. The results rule out the proposed symmetric multispin order parameters. The zero-field transition is found to exhibit critical softening of the spin gap and a cusp in the susceptibility at TN, as expected for the ordering of magnetic dipoles.