Critical Fluctuations and Disorder at the Vortex Liquid to Crystal Transition in Type-II Superconductors

TL;DR

This paper uses a functional renormalization group approach to analyze the vortex liquid to crystal transition in type-II superconductors, considering both pure and disordered systems, and suggests disorder may change the transition's nature.

Contribution

It extends FRG analysis to a generalized Landau-Ginzburg model with disorder, revealing fixed points and implications for the transition order in type-II superconductors.

Findings

Disorder introduces a stable fixed point for 1<n<4.

Pure system has a stable fixed point only for n>4.

Disorder likely changes the transition from first order to continuous.

Abstract

We present a functional renormalization group (FRG) analysis of a Landau-Ginzburg model of type-II superconductors (generalized to $n/2$ complex fields) in a magnetic field, both for a pure system, and in the presence of quenched random impurities. Our analysis is based on a previous FRG treatment of the pure case [E.Br\'ezin et. al., Phys. Rev. B, {\bf 31}, 7124 (1985)] which is an expansion in $\epsilon = 6-d$. If the coupling functions are restricted to the space of functions with non-zero support only at reciprocal lattice vectors corresponding to the Abrikosov lattice, we find a stable FRG fixed point in the presence of disorder for $1<n<4$, identical to that of the disordered $O(n)$ model in $d-2$ dimensions. The pure system has a stable fixed point only for $n>4$ and so the physical case ($n = 2$) is likely to have a first order transition. We speculate that the recent experimental findings that disorder removes the apparent first order transition are consistent with these calculations.