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

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.Brézin 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.

4 pages, no figures, typeset using revtex (v3.0)

References in corpus (2)

• Absence of a Phase Transition in a Three--Dimensional Vortex Glass Model with Screening
• Theory of a Continuous H${}_{c2}$ Normal-to-Superconducting Transition

Cited by in corpus (9)

• Theoretical Description of Resistive Behavior near a Quantum Vortex-Glass Transition
• Continuous 3d Freezing Transition in Layered Superconductors
• Parquet Graph Resummation Method for Vortex Liquids
• Non-perturbative approach to correlations in two-dimensional vortex liquids
• A Simple Analytical Model of Vortex Lattice Melting in 2D Superconductors
• Mixed phases in U(N) superconductivity
• Superconducting zero temperature phase transition in two dimensions and in the magnetic field
• Non-commutative field theory approach to two-dimensional vortex liquid system
• The Two-Dimensional Infinite Heisenberg Classical Square Lattice: Exact Theory and Experimental Results