Impact of long-range interactions on the disordered vortex lattice

TL;DR

This paper investigates how long-range vortex interactions in type-II superconductors influence the vortex lattice's behavior under disorder, revealing a crossover from logarithmic to sub-logarithmic displacement growth using a renormalization group approach.

Contribution

The study derives a flow equation for disorder correlations and predicts a crossover in displacement growth from logarithmic to sub-logarithmic at large distances.

Findings

Disorder-averaged displacement grows as ln^{2σ}(R/a_0)

Crossover from ln(R) to ln^{0.348}(R) growth at large distances

Long-range interactions suppress disorder effects in vortex lattices

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 \lambda and limits the above behavior to distances R<\lambda. 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^{2\sigma} (R/a_0). The logarithmic growth (2\sigma=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 2\sigma=0.348 at large distances.