Impact of long-range interactions on the disordered vortex lattice

Abstract

The interaction between the vortex lines in a type-II superconductor is mediated by currents. In the absence of transverse screening this interaction is long-ranged, stiffening up the vortex lattice as expressed by the dispersive elastic moduli. The effect of disorder is strongly reduced, resulting in a mean-squared displacement correlator <u^2(R,L)> = <[u(R,L)-u(0,0)]^2> characterized by a mere logarithmic growth with distance. Finite screening cuts the interaction on the scale of the London penetration depth λand limits the above behavior to distances R<λ. Using a functional renormalization group (RG) approach, we derive the flow equation for the disorder correlation function and calculate the disorder-averaged mean-squared relative displacement <u^2(R)> \propto ln^{2σ} (R/a_0). The logarithmic growth (2σ=1) in the perturbative regime at small distances [A.I. Larkin and Yu.N. Ovchinnikov, J. Low Temp. Phys. 34, 409 (1979)] crosses over to a sub-logarithmic growth with 2σ=0.348 at large distances.

9 pages, no figures

References in corpus (12)

• Creep and depinning in disordered media
• Elastic Theory of pinned flux lattices
• Vortex-glass phases in type-II superconductors
• Renormalization of pinned elastic systems: how does it work beyond one loop ?
• A Bragg glass phase in the vortex lattice of a type II superconductor
• Large N Expansion for 4-Epsilon Dimensional Oriented Manifolds in Random Media
• Disorder Driven Roughening Transitions of Elastic Manifolds and Periodic Elastic Media
• Nonuniversal Correlations and Crossover Effects in the Bragg-Glass Phase of Impure Superconductors
• (4+N)-Dimensional Elastic Manifolds in Random Media: a Renormalization-Group Analysis
• Roughening Transition of Interfaces in Disordered Systems
• Disordered periodic systems at the upper critical dimension
• Marginal pinning of vortices at high temperature