Correlation Lengths in the Vortex Line Liquid of a High-TcSuperconductor

Abstract

We use the three dimensional uniformly frustrated XY model, as a model for a high temperature superconductor in an applied magnetic field, to explicitly measure the longitudinal correlation length ξz in the vortex line liquid phase. We determine the scaling of ξz with magnetic field and system anisotropy close to the vortex lattice melting transition. We apply our results to determine the extent of longitudinal correlations in YBCO just above melting. 64. 60-i, 74.60-w, 74.76-w It is now generally accepted that thermal fluctuations in the high T c superconductors lead, for a clean sample in the mixed state, to a first order melting of the vortex line lattice into a vortex line liquid. Nordborg and Blatter [7] within the "two dimensional (2D) boson" approximation, as well as general theoretical considerations [8], predict a correlation length ξ z ∼ γ −1 a v , where γ ≡ λ z /λ ⊥ is the anisotropy ratio and a v = φ 0 /B is the average spacing between vortex lines. However analyses of experiments on untwinned single crystal YBCO by Righi et al. [9] and by Moore [10] have suggested that longitudinal correlations may be of the surprisingly larger micron scale.To investigate this issue, we carry out extensive new simulations of the frustrated 3D XY model for different values of applied flux density f and anisotropy η, explicitly measuring the longitudinal correlation length ξ z as determined by several different criteria. We find a good scaling of ξ z with f and η in the continuum limit, allowing us to estimate ξ z (T c ) in real YBCO single crystal samples. We find that longitudinal correlations at melting are enhanced with respect to the 2D boson approximation, but not dramatically so. We also address several additional questions. We show, contrary to recent claims [11], that there is only a single transition even in the isotropic model. In the very anisotropic limit ξ z (T c ) < d, where a cross over to 2D behavior has been predicted [8,12], we find no qualitative differences from the less anisotropic cases. We find that thermally excited vortex loops, which become important at low magnetic fields, can be described by an effective renormalization of the interaction between field induced vortex lines, and we find no evidence for a recently proposed transition within the vortex line liquid phase [13,14].Our model is the uniformly frustrated 3D XY model [15], given by the Hamiltonianwhere the sum is over the sites i of a cubic grid of points with unit basis vectorsμ =x,ŷ,ẑ. θ i is the phase angle of the superconducting wavefunction on site i, andA · dl is the integral of the magnetic vector potential on the specified bond. The unit of the grid spacing alongẑ is taken as d, the spacing between the weakly coupled CuO planes; the unit of the grid spacing in the xy plane is taken as ξ ⊥0 , the bare vortex core size in the plane. The Hamiltonian (1) results from making the London approximation to the discretized GinzburgLandau energy, and assuming λ/a v → ∞ so that the internal magnetic field B can be taken as frozen...

Topological phase fluctuations, amplitude fluctuations, and criticality in extreme type-II superconductors

“…Such a transition would have has its hallmark that the superfluid stiffness along the magnetic field, or equivalently the he-licity modulus Υ z , would vanish inside the vortex-liquid phase. This has now been conclusively demonstrated not to be the case [12][13][14]96 .…”

Vortex-glass phases in type-II superconductors

“…This signals a cross-over to a second critical regime with (probably) inverted XY behaviour (Helfrich andMüller 1980, Dasgupta andHalperin 1981). In this asymptotic regime λ and ξ scale in the same way with the correlation exponent ν XY (Olsson and Teitel 1999). It should be mentioned, however, that other scenarios have been proposed (for a recent discussion of earlier results see Kiometzis et al (1995), Radzihovsky (1995a), Herbut and Tešanović (1996), Herbut (1997), Folk and Holovatch (1999), Nguyen and Sudbø (1999)).…”

“…with respect to the zero-field critical region, but is still too small to describe the difference between H MF c2 (T ) and the melting line, Feigelman et al (1993) have argued that between the Abrikosov lattice and the normal phase there may be an intermediate liquid phase which still shows longitudinal superconductivity. We will not follow this idea here since more recent extensive simulations show only a single transition between the Abrikosov and the normal phase (Hu et al 1997, Hu et al 1998, Nguyen and Sudbø 1998, Nordborg and Blatter 1997, Nordborg and Blatter 1998, Olsson and Teitel 1999, although further proposals for an intermediate phase were made recently (Tešanović 1999, Nguyen andSudbø 1999).…”

Decoupled two-dimensional superconductivity and continuous melting transitions in layered superconductors immersed in a parallel magnetic field

“…The Hamiltonian is the so-called anisotropic, frustrated XY model on the superconductivity order parameter, where the frustrations in phase variables are induced by the magnetic field. This model has been used to simulate quite successfully the melting phenomenon of Abrikosov (or pancake) vortex lattice under magnetic fields parallel to the c axis [30,31,32,33,34,35]. We adopt the same model in the present study on interlayer Josephson vortices.…”