Dynamic and static properties of the randomly pinned planar flux array.

We report the results of large scale numerical studies of the dynamic and static properties of the random phase model of the randomly pinned flux lines confined in a plane. From the onset of nonlinear IV characteristics, we identify a vortex glass transition at the theoretically anticipated temperature. However, the vortex glass phase itself is much less glassy than expected. No signature of the glass transition has been detected in the static quantities measured. Typeset using REVTEX 1 Flux pinning is crucial to the performance of high-Tc superconductors in a strong magnetic field [1]. It has been conjectured [2,3] that flux lines in a superconductor with random, point-like impurities may form a glass, the vortex glass, in which the flux line configurations are frozen by the defects at low temperatures. It is argued [3,4] that if a glass phase exists, then the sluggish glassy dynamics of the flux lines suppresses dissipation, making the system a true superconductor. Unfortunately, evidence supporting the vortex glass hypothesis is still inconclusive: The phase transition seen experimentally by Koch et al [5] and by Gammel et al [6] may be due to pinning by correlated defects [7] such as twin planes and/or screw dislocations. Existing numerical simulations which support the existence of the vortex glass are thus far restricted to models with zero external magnetic field and/or an infinite London penetration length [8]. However, the glass phase seems to be unstable to thermal fluctuations in more realistic models with a finite London penetration length [9]. Without solid evidence from experimental and numerical studies, major support for the vortex glass hypothesis comes from a number of analytic studies [2,4,10,11], which are however restricted to “elastic systems” where topological defects are forbidden to nucleate. While the validity of the elastic approximation for the bulk system in 2+1 dimensions is a subject of intense current research, the elastic model is well justified to describe flux lines confined in a plane (1 + 1 dimensions) [2,12,13] or vortex lines in planar Josephson junctions [14]. Thus far, the 1 + 1 dimensional flux array is the only system for which a vortex glass phase has been demonstrated analytically; as such, it is one of the very few pieces of “solid” support on which the vortex glass hypothesis for bulk superconductors is based. Because of this significance, the static and dynamic properties of the 1 + 1 dimensional system have been investigated analytically by many groups in the past several years [2,10–17,?,19–22]. These studies led to a number of rather different predictions, none of which has been tested experimentally or numerically. In this paper, we report the results of detailed numerical studies of the random phase model [2,12,14,23] of the planar flux array using the Connection Machine CM5. We observe an apparent vortex glass transition at a finite temperature, Tg, below which the IV 2 characteristics are nonlinear and described by power laws, as anticipated by Refs. [12] and [16]. However, the universal constant found is significantly smaller than that predicted in Ref. [16]. Static quantities such as the equal-time correlation function are also measured. They exhibit no detectable signs of the glass transition. We consider an array of flux lines confined to the (x, z)-plane, and directed in the zdirection by an applied magnetic field H = H0ẑ [23]. Line-line repulsion is modeled by linear elasticity, with an elastic constant κ = (dρ/dH0) , where ρ is the average line density. Random point-like pinning centers in the plane are described by an uncorrelated Gaussian random potential with a variance ∆0. A direct simulation of the flux array is deemed difficult because an interline spacing of ρ ∼ 10 grid points and a system size of ≫ 10ρ is needed to probe the asymptotic behavior. Instead we will study the random phase model,