Vortex Entanglement and Broken Symmetry

Based on the London approximation, we investigate numerically the stability of the elementary configurations of entanglement, the twisted-pair and the twisted-triplet, in the vortex-lattice and -liquid phases. We find that, except for the dilute limit, the twisted-pair is unstable and hence irrelevant in the discussion of entanglement. In the lattice phase the twisted-triplet constitutes a metastable, confined configuration of high energy. Loss of lattice symmetry upon melting leads to deconfinement and the twisted-triplet turns into a low-energy helical configuration.Comment: 4 pages, RevTex, 2 figures on reques

Weak- to strong pinning crossover

Material defects in hard type II superconductors pin the flux lines and thus establish the dissipation-free current transport in the presence of a finite magnetic field. Depending on the density and pinning force of the defects and the vortex density, pinning is either weak-collective or strong. We analyze the weak- to strong pinning crossover of vortex matter in disordered superconductors and discuss the peak effect appearing naturally in this context.Comment: 4 pages, 2 figure

Local mapping of dissipative vortex motion

We explore, with unprecedented single vortex resolution, the dissipation and motion of vortices in a superconducting ribbon under the influence of an external alternating magnetic field. This is achieved by combing the phase sensitive character of ac-susceptibility, allowing to distinguish between the inductive-and dissipative response, with the local power of scanning Hall probe microscopy. Whereas the induced reversible screening currents contribute only inductively, the vortices do leave a fingerprint in the out-of-phase component. The observed large phase-lag demonstrates the dissipation of vortices at timescales comparable to the period of the driving force (i.e. 13 ms). These results indicate the presence of slow microscopic loss mechanisms mediated by thermally activated hopping transport of vortices between metastable states.Comment: 5 pages, 2 figure

Depinning transition of dislocation assemblies: pileup and low-angle grain boundary

We investigate the depinning transition occurring in dislocation assemblies. In particular, we consider the cases of regularly spaced pileups and low angle grain boundaries interacting with a disordered stress landscape provided by solute atoms, or by other immobile dislocations present in non-active slip systems. Using linear elasticity, we compute the stress originated by small deformations of these assemblies and the corresponding energy cost in two and three dimensions. Contrary to the case of isolated dislocation lines, which are usually approximated as elastic strings with an effective line tension, the deformations of a dislocation assembly cannot be described by local elastic interactions with a constant tension or stiffness. A nonlocal elastic kernel results as a consequence of long range interactions between dislocations. In light of this result, we revise statistical depinning theories and find novel results for Zener pinning in grain growth. Finally, we discuss the scaling properties of the dynamics of dislocation assemblies and compare theoretical results with numerical simulations.Comment: 13 pages, 8 figure

Depinning transition of dislocation assemblies: pileup and low-angle grain boundary

We investigate the depinning transition occurring in dislocation assemblies. In particular, we consider the cases of regularly spaced pileups and low angle grain boundaries interacting with a disordered stress landscape provided by solute atoms, or by other immobile dislocations present in non-active slip systems. Using linear elasticity, we compute the stress originated by small deformations of these assemblies and the corresponding energy cost in two and three dimensions. Contrary to the case of isolated dislocation lines, which are usually approximated as elastic strings with an effective line tension, the deformations of a dislocation assembly cannot be described by local elastic interactions with a constant tension or stiffness. A nonlocal elastic kernel results as a consequence of long range interactions between dislocations. In light of this result, we revise statistical depinning theories and find novel results for Zener pinning in grain growth. Finally, we discuss the scaling properties of the dynamics of dislocation assemblies and compare theoretical results with numerical simulations.Comment: 13 pages, 8 figure

Topological Defects in the Abrikosov Lattice of Vortices in Type-II Superconductors

The free energy costs for various defects within an Abrikosov lattice of vortices are calculated using the lowest Landau level approximation (LLL). Defect solutions with boundary conditions for lines to meet at a point (crossing defect) and for lines to twist around each other (braid defect) are sought for 2, 3, 6, and 12 lines. Many results have been unexpected, including the nonexistence of a stable two- or three-line braid. This, and the high energy cost found for a six-line braid lead us to propose that the equilibrium vortex state is not entangled below the irreversibility line of the high-$T_c$ superconductors or in a large part of the vortex-liquid phase above this line. Also, the solution for an infinite straight screw dislocation is found, and used to give a limiting form for the free energy cost of very large braids. This depends on the area enclosed by the braid as well as its perimeter length.Comment: 30 pages, 17 Encapsulated PostScript figures, uses Revtex (with epsf

Campbell Penetration Depth of a Superconductor in the Critical State

The magnetic penetration depth $\lambda(T,H,j)$ was measured in the presence of a slowly relaxing supercurrent, $j$. In single crystal $\mathrm{Bi_2Sr_2CaCu_2O_8}$ below approximately 25 K, $\lambda(T,H,j)$ is strongly hysteretic. We propose that the irreversibility arises from a shift of the vortex position within its pinning well as $j$ changes. The Campbell length depends upon the ratio $j/j_{c}$ where $j_{c}$ is the critical current defined through the Labusch parameter. Similar effects were observed in other cuprates and in an organic superconductor

A general scaling relation for the critical current density in Nb3Sn

We review the scaling relations for the critical current density (Jc) in Nb3Sn wires and include recent findings on the variation of the upper critical field (Hc2) with temperature (T) and A15 composition. We highlight deficiencies in the Summers/Ekin relations, which are not able to account for the correct Jc(T) dependence. Available Jc(H) results indicate that the magnetic field dependence for all wires can be described with Kramer's flux shear model, if non-linearities in Kramer plots are attributed to A15 inhomogeneities. The strain (eps) dependence is introduced through a temperature and strain dependent Hc2*(T,eps) and Ginzburg- Landau parameter kappa1(T,eps) and a strain dependent critical temperature Tc(eps). This is more consistent than the usual Ekin unification, which uses two separate and different dependencies on Hc2*(T) and Hc2*(eps). Using a correct temperature dependence and accounting for the A15 inhomogeneities leads to a remarkable simple relation for Jc(H,T,eps). Finally, a new relation for s(eps) is proposed, based on the first, second and third strain invariants.Comment: Accepted Topical Review for Superconductor, Science and Technolog

Low field vortex dynamics over seven time decades in a Bi_2Sr_2CaCu_2O_{8+\delta} single crystal for temperatures 13 K < T < 83 K

Using a custom made dc-SQUID magnetometer, we have measured the time relaxation of the remanent magnetization M_rem of a Bi_2Sr_2CaCu_2O_{8+\delta} single crystal from the fully critical state for temperatures 13 K < T < 83 K. The measurements cover a time window of seven decades 10^{-2} s < t < 10^5 s, so that the current density j can be studied from values very close to j_c down to values considerably smaller than j_c. From the data we have obtained: (i) the flux creep activation barriers U as a function of current density j, (ii) the current-voltage characteristics E(j) in a typical range of 10^{-7} V/cm to 10^{-15} V/cm, and (iii) the critical current density j_c(0) at T = 0. Three different regimes of vortex dynamics are observed: For temperatures T < 20 K the activation barrier U(j) is logarithmic, no unique functional dependence U(j) could be found for the intermediate temperature interval 20 K < T < 40 K, and finally for T > 40 K the activation barrier U(j) follows a power-law behavior with an exponent mu = 0.6. From the analysis of the data within the weak collective pinning theory for strongly layered superconductors, it is argued that for temperatures T < 20 K pancake-vortices are pinned individually, while for temperatures T > 40 K pinning involves large collectively pinned vortex bundles. A description of the vortex dynamics in the intermediate temperature interval 20 K < T < 40 K is given on the basis of a qualitative low field phase diagram of the vortex state in Bi_2Sr_2CaCu_2O_{8+\delta}. Within this description a second peak in the magnetization loop should occur for temperatures between 20 K and 40 K, as it has been observed in several magnetization measurements in the literature.Comment: 12 pages, 10 figure

Time Resolved Stroboscopic Neutron Scattering of Vortex Lattice Dynamics in Superconducting Niobium

Superconducting vortex lattices, glasses and liquids attract great interest as model systems of crystallization and as a source of microscopic information of the nature of superconductivity. We report for the first time direct microscopic measurements of the vortex lattice tilt modulus c44 in ultra-pure niobium using time-resolved small angle neutron scattering. Besides a general trend to faster vortex lattice dynamics for increasing temperatures we observe a dramatic changeover of the relaxation process associated with the non-trivial vortex lattice morphology in the intermediate mixed state. This changeover is attributed to a Landau-branching of the Shubnikov domains at the surface of the sample. Our study represents a showcase for how to access directly vortex lattice melting and the formation of vortex matter states for other systems.Comment: 14 pages, 14 figure