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Register a new userExact analytic Gorkov-Ginzburg-Landau theory of type-II superconductivity in the magneto-quantum oscillations limit
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A new Greens function representation is employed in a microscopic derivation of a Ginzburg-Landau theory of strongly type superconductivity at high magnetic fields. An exact analytical, physically transparent expression for the quartic term in the corresponding order parameter expansion is presented. The resulting expression reveals singular non-local contributions to the superconducting (SC) free energy, associated with highly coherent cyclotron motions of the paired electrons near the Fermi surface, which are strongly coupled to the vortex lattice. A major part of these contributions arises from incoherent scattering by the spatially averaged pair-potential, which is purely harmonic in the de Haas van Alphen frequency. However, coherent scatterings by the ordered vortex lattice generate, at low temperatures, large erratically oscillating (i.e. paramagnetic-diamagnetic) contribution to the SC free energy as a function of the magnetic field. Vortex lattice disorder, which tends to suppress this oscillatory component, is found to preserve the singular harmonic part of the SC free energy.
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Since the concept of spin superconductor was proposed, all the related studies concentrate on spin-polarized case. Here, we generalize the study to spin-non-polarized case. The free energy of non-polarized spin superconductor is obtained, and the Ginzburg-Landau-type equations are derived by using the variational method. These Ginzburg-Landau-type equations can be reduced to the spin-polarized case when the spin direction is fixed. Moreover, the expressions of super linear and angular spin currents inside the superconductor are derived. We demonstrate that the electric field induced by super spin current is equal to the one induced by equivalent charge obtained from the second Ginzburg-Landau-type equation, which shows self-consistency of our theory. By applying these Ginzburg-Landau-type equations, the effect of electric field on the superconductor is also studied. These results will help us get a better understanding of the spin superconductor and the related topics such as Bose-Einstein condensate of magnons and spin superfluidity.
In the Ginzburg-Landau theory of superfluid $^{3}$He, the free energy is expressed as an expansion of invariants of a complex order parameter. Strong coupling effects, which increase with increasing pressure, are embodied in the set of coefficients of these order parameter invariantscite{Leg75,Thu87}. Experiments can be used to determine four independent combinations of the coefficients of the five fourth order invariants. This leaves the phenomenological description of the thermodynamics near $T_{c}$ incomplete. Theoretical understanding of these coefficients is also quite limited. We analyze our measurements of the magnetic susceptibility and the NMR frequency shift in the $B$-phase which refine the four experimental inputs to the phenomenological theory. We propose a model based on existing experiments, combined with calculations by Sauls and Serenecite{Sau81} of the pressure dependence of these coefficients, in order to determine all five fourth order terms. This model leads us to a better understanding of the thermodynamics of superfluid $^{3}$He in its various states. We discuss the surface tension of bulk superfluid $^{3}$He and predictions for novel states of the superfluid such as those that are stabilized by elastic scattering of quasiparticles from a highly porous silica aerogel.
Long-standing discrepancies within determinations of the Ginzburg-Landau parameter $kappa$ from supercritical field measurements on superconducting microspheres are reexamined. The discrepancy in tin is shown to result from differing methods of analyses, whereas the discrepancy in indium is a consequence of significantly differing experimental results. The reanalyses however confirms the lower $kappa$ determinations to within experimental uncertainties.
We report the discovery of superconductivity in the ternary aluminide Nb$_{5}$Sn$_{2}$Al, which crystallizes in the W$_{5}$Si$_{3}$-type structure with one-dimensional Nb chains along the $c$-axis. It is found that the compound has a multiband nature and becomes a weakly coupled, type-II superconductor below 2.0 K. The bulk nature of superconductivity is confirmed by the specific heat jump, whose temperature dependence shows apparent deviation from a single isotropic gap behavior. The lower and upper critical fields are estimated to be 2.0 mT and 0.3 T, respectively. From these values, we derive the penetration depth, coherence length and Ginzburg-Landau parameter to be 516 nm, 32.8 nm and 15.6, respectively. By contrast, the isostructural compound Ti$_{5}$Sn$_{2}$Al dose not superconduct above 0.5 K. A comparison of these results with other W$_{5}$Si$_{3}$-type superconductors suggests that $T_{rm c}$ of these compounds correlates with the average number of valence electrons per atom.
In this paper we show how, under certain restrictions, the hydrodynamic equations for the freely evolving granular fluid fit within the framework of the time dependent Landau-Ginzburg (LG) models for critical and unstable fluids (e.g. spinodal decomposition). The granular fluid, which is usually modeled as a fluid of inelastic hard spheres (IHS), exhibits two instabilities: the spontaneous formation of vortices and of high density clusters. We suppress the clustering instability by imposing constraints on the system sizes, in order to illustrate how LG-equations can be derived for the order parameter, being the rate of deformation or shear rate tensor, which controls the formation of vortex patterns. From the shape of the energy functional we obtain the stationary patterns in the flow field. Quantitative predictions of this theory for the stationary states agree well with molecular dynamics simulations of a fluid of inelastic hard disks.
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