Singular and Nonsingular Vortex Structures in High-Temperature Superconductors

A model for flux creep in terms of a distribution of pinning centres which are random in space is presented, leading to expressions for the magnetic relaxation and the voltage-current characteristic. Special emphasis is given to the possibility of history effects due to the relaxation of non-steady-state distributions of magnetic flux. A treatment using a time-dependent annealing function is presented.

Critical conditions are obtained for bifurcation phenomena in nonequilibrium systems (chemical instabilities) which are appropriate for transitions between homogeneous steady states as well as for symmetry-breaking transitions to static structures. In the case of symmetry-breaking instabilities these criteria enable the theory to be applied to systems in any number of spatial dimensions, eliminating a restriction to one-dimensional systems encountered in other treatments. These critical conditions allow for the derivation of time-dependent Ginzburg-Landau (TDGL)-type equations for the critical-mode amplitude (the order parameter) that grows into the new macrostate beyond the critical point. For homogeneous transitions the usual TDGL equation is obtained. For the case of intrinsic symmetry breaking, TDGL equations are found for coupled order parameters corresponding to different directions in $k$ space. In both the intrinsic and the extrinsic cases the TDGL equations are found to have nonlinear transport terms. When the TDGL equations are turned into Langevin equations, Ginzburg criteria (defining the region where meanfield theory breaks down) are derived. The critical dimensionality thus determined is 4 for homogeneous and intrinsic symmetry-breaking transitions, and 6 for the extrinsic symmetry-breaking case (under given mild technical conditions). Expressions for the size of the nonclassical critical regions are obtained for the different transitions in terms of characteristic parameters. For chemical instabilities these regions are in principle accessible.

The Hall effect in the vortex state of ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$ single-crystal thin films has been measured from the underdoped to the overdoped regime ($x=0.1\ensuremath{-}0.24$). The Hall sign reversal is observed in the underdoped and slightly overdoped samples, while it is absent in the overdoped samples. This is consistent with the recent theory based on the time-dependent Ginzburg-Landau equation, which predicts that the sign reversal is related to the electronic state at the Fermi level. The field dependence of Hall conductivity ${\ensuremath{\sigma}}_{\mathrm{xy}}$ can be expressed as ${\ensuremath{\sigma}}_{\mathrm{xy}}=\frac{{C}_{1}}{H}+{C}_{2}+{C}_{3}H$, where ${C}_{1}$ and ${C}_{3}$ terms are associated with vortex motion and quasiparticle Hall effect in the vortex core, respectively. It appears that the field-independent term ${C}_{2}$ becomes appreciable with increasing anisotropy.

The structure of vortices in Bose-Einstein condensed atomic gases is studied\ntaking into account many-body correlation effects. It is shown that for excited\nvortices the particle density in the vortex core increases as the angular\nmomentum of the system increases. The core density can increase by several\ntimes with only a few percent change in the angular momentum. This result\nprovides an explanation for the observations in which the measured angular\nmomentum is higher than the estimation based on counting the number of\nvortices, and the visibility of the vortex cores is simultaneously reduced. The\ncalculated density profiles for the excited vortices are in good agreement with\nexperimental measurements.\n

Preface. Part I: Cuprate superconductivity. Growth and doping of MBE prepared cuprate films I. Lagues, et al. Growth of a hard-grown single crystal-Bi2SR2Ca2O10+delta C.T. Lin, B. Liang. Exchange and spinfluctuation pairing in the two-band Hubbard model Applications to cuprate N.M. Plakida. High temperatures superconductors in high frequency fields C.T. Rieck, K. Scharnberg. Stripe-like inhomogeneities, carriers, and BCS-BEC crossover in the high Tc cuprates J. Ashkenazi. Charge- and spin-density-wave superconductors: Psuedogap puzzle in the cuprates A.M. Gabovich, et al. Strong-coupling superconductivity with d-wave order parameter and s-wave gap applications to cuprates A.S. Alexandrov. Theory of BSCCO bicrystal C-axis twist Josephson junctions: a new phase-sensitive test of order parameter symmetry R.M. Klemm. Time reversal breaking states and spontaneous current patterns in Josephson junction of d-wave superconductors M.H.S. Amin. Electronic thermal conductivity of partially-gapped CDW superconductors M. Ausloos. Peculiarities of the spectrum of strongly correlated electrons A. Sherman, M. Schreiber. Pair-transfer superconductivity on doping determined bands and the pseudogap N. Kristoffel, P. Rubin. Extended Brinkman-Rice picture and its application to high-Tc superconductors H.-T. Kim. Many band effects in superconductivity H. Nagao et al. Study on electronic specific heat of La2-XSrxCuO4: pseudogap and superconductivity N. Momono, et al. Correlation between superconducting gap and pseudogap in High-Tc cooperates M. Oda, et al. High spin paramagnetic centers in tetragonal phase of Er123, Dy123, and (er,Y)123 compounds V. Likodimos, et al. EPR study of spin clusters in oxygen deficient R123 compounds V. Likodimos, et al. Part II: Novel superconductors. Superconductivity in pure and electron-doped MgB2: transport properties and pressure effects B. Lorenz, et al. Superconductivity gap and electron-phonon interaction in MgB2 thin film studied by point contact N.L. Bobrov. A two-band approach to MgB2 superconductivity T. Ord, N. Kristoffel. Specific heat and disorder in the mixed state of non-magnetic borocarbides and a comparison with exotic superconductors D. Lipp, et al. On the influence of a non-local electrodynamics in the irreversible magnetization of non-magnetic borocarbides A.V. Silhanek. Spontaneous spin polarization and electronic states in platinum nano-particles towards compacted superconductivity H. Hori. Calculation of correlation functions for superconductivity models N.N. Bogolubov. Theoretical analysis of the symmetry of the order parameter in unconventional superconductors: singlet versus triplet pairing D. Manske. P-wave pairing in superconducting Sr2RuO4 Litak. High temperatures superconductivity of semi-localized 2D electron system with circular molecular orbits M. Sugahara. Two- particle green function in the theory of superconductivity of HTSC and C60 crystals A.M. Yaremko. Part III: Mesoscopic Superconductors. Vortex structure in mesoscopic superconductors F.M. Peeters, B.J. Baelus. Quantum measurement of charge and flux qubits Y. Makhlin. Nanostructured superconductor/ferromagnet bilayers M. Lange, et al. Half-integer number vortices in the Ginzburg-Landau-Higgs model G. Stenuit, et al. The hydrodynamic instability in the

Time-dependent Ginzburg–Landau equation in a car-following model considering the driver’s physical delay

The transport properties in the mixed state of high-quality Ca0.8La0.2Fe0.98Co0.02As2 single crystal, a newly discovered 112-type iron pnictide superconductor, are comprehensively studied by magneto-resistivity measurement. The field-dependent activation energy, U0, is derived in the framework of thermally activated flux flow (TAFF) theory, yielding a power law dependence U0~Hα with a crossover at a magnetic field around 2 T in both H⊥ab and H//ab, which is ascribed to the different pinning mechanisms. Moreover, we have clearly observed the vortex phase transition from vortex-glass to vortex-liquid according to the vortex-glass model, and vortex phase diagrams are constructed for both H⊥ab and H//ab. Finally, the results of mixed-state Hall effect show that no sign reversal of transverse resistivity ρxy(H) is detected, indicating that the Hall component arising from the vortex flow is also negative based on the time dependent Ginzburg-Landau (TDGL) theory. Meanwhile, the transverse resistivity ρxy(H) and the longitudinal resistivity ρxx(H) follow the relation |ρxy(H)|=Aρxx(H)β well with an exponent β~2.0, which is in line with the results in theories or experiments previously reported on some high-Tc cuprates.

The electromagnetic response to microwaves in the mixed state of\nYBa2Cu3Oy(YBCO) was measured in order to investigate the electronic state\ninside and outside the vortex core. The magnetic-field dependence of the\ncomplex surface impedance at low temperatures was in good agreement with a\ngeneral vortex dynamics description assuming that the field-independent viscous\ndamping force and the linear restoring force were acting on the vortices. In\nother words, both real and imaginary parts of the complex resistivity, \\rho_1,\nand \\rho_2, were linear in B. This is explained by theories for d-wave\nsuperconductors. Using analysis based on the Coffey-Clem description of the\ncomplex penetration depth, we estimated that the vortex viscosity \\eta at 10 K\nwas (4 \\sim 5) \\times 10^{-7} Ns/m^2. This value corresponds to \\omega_0 \\tau\n\\sim 0.3 - 0.5, where \\omega_0 and \\tau are the minimal gap frequency and the\nquasiparticle lifetime in the vortex core, respectively. These results suggest\nthat the vortex core in YBCO is in the moderately clean regime. Investigation\nof the moderately clean vortex core in high-temperature superconductors is\nsignificant because physically new effects may be expected due to d-wave\ncharacteristics and to the quantum nature of cuprate superconductors. The\nbehavior of Z_s as a function of B across the first order transition (FOT) of\nthe vortex lattice was also investigated. Unlike Bi2Sr2CaCu2Oy (BSCCO), no\ndistinct anomaly was observed around the FOT in YBCO. Our results suggest that\nthe rapid increase of X_s due to the change of superfluid density at the FOT\nwould be observed only in highly anisotropic two-dimensional vortex systems\nlike BSCCO. We discuss these results in terms of the difference of the\ninterlayer coupling and the energy scale between the two materials.\n

We study the hydrodynamics of superconductors within the framework of Schwinger-Keldysh effective field theory (EFT). We show that in the vicinity of the superconducting phase transition the most general leading-order EFT satisfying the local Kubo-Martin-Schwinger condition is described by a version of the time-dependent Ginzburg-Landau (TDGL) equations augmented with stochastic terms. This version of TDGL is applicable in the gapless regime independent of any microscopic details. Within this approach, it is possible to include systematically the effects of nonuniform temperature and heat conductivity, as well as explicit or spontaneous breaking of time reversal. We also introduce a thermal version of the Josephson relation and use it to construct an exotic hydrodynamics describing a phase of matter where heat can flow without dissipation.

PurposeThe purpose of this paper is to investigate the development process of the fire whirl in the fixed-frame facility and focus on the impacts of the fire whirl’s vortex core on the formation and flame structure of the fire whirl.Design/methodology/approachThe complex turbulent reacting flame surface is captured by the large eddy simulation turbulence closure coupled with two sub-grid scale (SGS) kinetic schemes (i.e. the chemistry equilibrium and steady diffusion flamelet). Numerical predictions are validated thoroughly against the measurements by Lei et al. (2015) with excellent agreements. A double maximum tangential velocity refinement approach is proposed to quantify the vortex cores’ instantaneous location and region, addressing the missing definition in other studies.FindingsThe numerical results show that the transition process of the fire whirl is dominated by the vortex core movement, which is related to the centripetal force. The unsteadiness of the fully developed fire whirl was found depending on the instantaneous fluctuation of heat release rate. The steady diffusion flamelet scheme is essential to capture the instantaneous fluctuation. Furthermore, the axial velocity inside the vortex core is the key to determining the state of fire whirl.Practical implicationsDue to intensive interactions between buoyant fires and ambient rotating flow, the on-set and formation of fire whirl still remain largely elusive. This paper focused on the transition process of fire whirl between different development stages. This paper provides insights into the transition process from the inclined flame to the fire whirls based on the centripetal force.Originality/valueThis paper presented and compared two SGS kinetic schemes to resolve the fire whirl development process and the unsteadiness of its vortical structures. The modelling framework addresses the shortcoming of previous numerical studies where RANS turbulence closure and simplified combustion kinetics was adopted. Numerical results also revealed the fire whirl transition process and its relationship to centripetal force.

A series of blade tip geometries, including original plain tip, rounded tip on the pressure side and diverging tip towards the suction side, were adopted to investigate the effect of blade geometry on tip leakage vortex dynamics and cavitation pattern in an axial-flow pump. On the basis of the computation, it clearly shows the flow structure in the clearance for different tip configurations by the detailed data of axial velocity and turbulent kinetic energy. The in-plain trajectory, in aspects of the angle between the blade suction side and vortex core and the initial point of tip leakage vortex, was presented using the maximum swirling strength method. The most striking feature is that the inception location of tip leakage vortex is delayed for chamfered tip due to the change of blade loading on suction side. Some significant non-dimensional parameters, such as pressure, swirling strength and turbulent kinetic energy, were used to depict the characteristics of tip vortex core. By the distribution of circumferential vorticity which dominates the vortical flows near the tip region, it is observed that the endwall detachment as the leakage flow meets the mainstream varies considerably for tested cases. The present study also indicates that the shear layer feeds the turbulence into tip leakage vortex core, but the way is different. For the chamfered tip, high turbulence level in vortex core is mainly from the tip clearance where large turbulent kinetic energy emerges, while it is almost from a layer extending from the suction side corner for rounded tip. At last, the visualized observations show that tip clearance cavitation is eliminated dramatically for rounded tip but more intensive for chamfered tip, which can be associated with the vortex structure in the clearance.

We apply the complete nonlinear Time Dependent Ginzburg Landau (TDGL) equations to study the vortex dynamics in a mesoscopic type II superconductor using the numerical method based on the technique of gauge invariant variables. The solution of these equations shows how the vorticity penetrates into and goes out of the superconductor through the surface boundary. We calculate the spatial distribution of the superconducting electron density and the phase of the superconducting order parameter in a mesoscopic superconducting square sample containing two holes in the presence of a uniform perpendicular magnetic field. The dynamics of different vortex states are studied as a function of the external magnetic field.

The effect of a high electric field on the c-axis fluctuation conductivity in layered superconductors near the superconducting transition is investigated by the time-dependent Ginzburg-Landau equation. The c-axis fluctuation conductivity is calculated in self-consistent Gaussian approximation for an arbitrarily strong electric field and a magnetic field perpendicular to the layers. Our results include all Landau levels and have refined analytical form. The results in linear response are in good agreement with the experimental data in a wide region around T c in high T c superconductor. We also show that high electric fields can be effectively used to suppress the c-axis fluctuation conductivity in high-temperature superconductors.

Classical solutions of general ginzburg-landau equations

Jamming transition of high-dimensional traffic dynamics