Localized Flux Lines and the Bose Glass

Columnar defects provide effective pinning centers for magnetic flux lines in high--$T_{\rm c}$ superconductors. Utilizing a mapping of the statistical mechanics of directed lines to the quantum mechanics of two--dimensional bosons, one expects an entangled flux liquid phase at high temperatures, separated by a second--order localization transition from a low--temperature ``Bose glass'' phase with infinite tilt modulus. Recent decoration experiments have demonstrated that below the matching field the repulsive forces between the vortices may be sufficiently large to produce strong spatial correlations in the Bose glass. This is confirmed by numerical simulations, and a remarkably wide soft ``Coulomb gap'' at the chemical potential is found in the distribution of pinning energies. At low currents, the dominant transport mechanism in the Bose glass phase proceeds via the formation of double kinks between not necessarily adjacent columnar pins, similar to variable--range hopping in disordered semiconductors. The strong correlation effects originating in the long--range vortex interactions drastically reduce variable--range hopping transport.Comment: 10 pages, latex ("lamuphys.sty" file included), 6 figures can be obtained from the author ([email protected]); to appear in Proc. XIV Sitges conference on "Complex Behaviour of Glassy Systems" (Springer--Verlag

Variational theory of flux-line liquids

We formulate a variational (Hartree like) description of flux line liquids which improves on the theory we developed in an earlier paper [A.M. Ettouhami, Phys. Rev. B 65, 134504 (2002)]. We derive, in particular, how the massive term confining the fluctuations of flux lines varies with temperature and show that this term vanishes at high enough temperatures where the vortices behave as freely fluctuating elastic lines.Comment: 10 pages, 1 postscript figur

Low-Temperatures Vortex Dynamics in Twinned Superconductors

We discuss the low-temperature dynamics of magnetic flux lines in samples with a family of parallel twin planes. A current applied along the twin planes drives flux motion in the direction transverse to the planes and acts like an electric field applied to {\it one-dimensional} carriers in disordered semiconductors. As in flux arrays with columnar pins, there is a regime where the dynamics is dominated by superkink excitations that correspond to Mott variable range hopping (VRH) of carriers. In one dimension, however, rare events, such as large regions void of twin planes, can impede VRH and dominate transport in samples that are sufficiently long in the direction of flux motion. In short samples rare regions can be responsible for mesoscopic effects.Comment: 4 pages, 2 figures email: [email protected]

Theory of Double-Sided Flux Decorations

A novel two-sided Bitter decoration technique was recently employed by Yao et al. to study the structure of the magnetic vortex array in high-temperature superconductors. Here we discuss the analysis of such experiments. We show that two-sided decorations can be used to infer {\it quantitative} information about the bulk properties of flux arrays, and discuss how a least squares analysis of the local density differences can be used to bring the two sides into registry. Information about the tilt, compressional and shear moduli of bulk vortex configurations can be extracted from these measurements.Comment: 17 pages, 3 figures not included (to request send email to [email protected]

Interstitials, Vacancies and Dislocations in Flux-Line Lattices: A Theory of Vortex Crystals, Supersolids and Liquids

We study a three dimensional Abrikosov vortex lattice in the presence of an equilibrium concentration of vacancy, interstitial and dislocation loops. Vacancies and interstitials renormalize the long-wavelength bulk and tilt elastic moduli. Dislocation loops lead to the vanishing of the long-wavelength shear modulus. The coupling to vacancies and interstitials - which are always present in the liquid state - allows dislocations to relax stresses by climbing out of their glide plane. Surprisingly, this mechanism does not yield any further independent renormalization of the tilt and compressional moduli at long wavelengths. The long wavelength properties of the resulting state are formally identical to that of the ``flux-line hexatic'' that is a candidate ``normal'' hexatically ordered vortex liquid state.Comment: 21 RevTeX pgs, 7 eps figures uuencoded; corrected typos, published versio

Topological Defects on Fluctuating Surfaces: General Properties and the Kosterlitz-Thouless Transition

We investigate the Kosterlitz-Thouless transition for hexatic order on a free fluctuating membrane and derive both a Coulomb gas and a sine-Gordon Hamiltonian to describe it. The Coulomb-gas Hamiltonian includes charge densities arising from disclinations and from Gaussian curvature. There is an interaction coupling the difference between these two densities, whose strength is determined by the hexatic rigidity, and an interaction coupling Gaussian curvature densities arising from the Liouville Hamiltonian resulting from the imposition of a covariant cutoff. In the sine-Gordon Hamiltonian, there is a linear coupling between a scalar field and the Gaussian curvature. We discuss gauge-invariant correlation function for hexatic order and the dielectric constant of the Coulomb gas. We also derive renormalization group recursion relations that predict a transition with decreasing bending rigidity $\kappa$.Comment: REVTEX, 45 pages with 11 postscript figures compressed using uufiles. Accepted for publication in Phys. Rev.

Victims of Progress: Economic Integration, Specialization, and Wages for Unskilled Labor

In this paper we demonstrate that intra-industry trade (or FDI) between identical countries could produce the observed deterioration in the relative wages of unskilled workers. This involves a model of North-North integration through either increased trade flows or increased MNE- based production. Our motivation in this regard is arguments to the effect that trade cannot be responsible for the observed labour market trends because trade with developing countries is quantitatively too small to have significant labour market effects. We also introduce a relatively unexploited class of model that possesses attractive properties with respect to the explicit incorporation of firm-theoretic considerations in trade models

Fluctuations and Intrinsic Pinning in Layered Superconductors

A flux liquid can condense into a smectic crystal in a pure layered superconductors with the magnetic field oriented nearly parallel to the layers. If the smectic order is commensurate with the layering, this crystal is {\sl stable} to point disorder. By tilting and adjusting the magnitude of the applied field, both incommensurate and tilted smectic and crystalline phases are found. We discuss transport near the second order smectic freezing transition, and show that permeation modes lead to a small non--zero resistivity and large but finite tilt modulus in the smectic crystal.Comment: 4 pages + 1 style file + 1 figure (as uufile) appended, REVTEX 3.

Properties of the Bose glass phase in irradiated superconductors near the matching field

Structural and transport properties of interacting localized flux lines in the Bose glass phase of irradiated superconductors are studied by means of Monte Carlo simulations near the matching field B_Phi, where the densities of vortices and columnar defects are equal. For a completely random columnar pin distribution in the xy-plane transverse to the magnetic field, our results show that the repulsive vortex interactions destroy the Mott insulator phase which was predicted to occur at B = B_Phi. On the other hand, for ratios of the penetration depth to average defect distance lambda/d <= 1, characteristic remnants of the Mott insulator singularities remain visible in experimentally accessible quantities as the magnetization, the bulk modulus, and the magnetization relaxation, when B is varied near B_Phi. For spatially more regular disorder, e.g., a nearly triangular defect distribution, we find that the Mott insulator phase can survive up to considerably large interaction range \lambda/d, and may thus be observable in experiments.Comment: RevTex, 17 pages, eps files for 12 figures include

Hydrodynamics of liquids of arbitrarily curved flux-lines and vortex loops

We derive a hydrodynamic model for a liquid of arbitrarily curved flux-lines and vortex loops using the mapping of the vortex liquid onto a liquid of relativistic charged quantum bosons in 2+1 dimensions recently suggested by Tesanovic and by Sudbo and collaborators. The loops in the flux-line system correspond to particle-antiparticle fluctuations in the bosons. We explicitly incorporate the externally applied magnetic field which in the boson model corresponds to a chemical potential associated with the conserved charge density of the bosons. We propose this model as a convenient and physically appealing starting point for studying the properties of the vortex liquid