Non-Universal Quasi-Long Range Order in the Glassy Phase of Impure Superconductors

TL;DR

This paper systematically analyzes the structural correlations of disordered Abrikosov lattices, revealing non-universal quasi-long-range order and distinct scaling regimes influenced by elastic constants, challenging previous variational approaches.

Contribution

It provides the first systematic RG calculation of correlation functions in disordered flux line lattices, showing non-universal exponents and multiple scaling regimes.

Findings

Abrikosov lattice exhibits non-universal quasi long-range order.

Three distinct scaling regimes identified: Larkin, manifold, and Bragg glass.

Exponents depend on the ratio of elastic constants, differing from variational predictions.

Abstract

The structural correlation functions of a weakly disordered Abrikosov lattice are calculated for the first time in a systematic RG-expansion in d=4-\epsilon dimensions. It is shown, that in the asymptotic limit the Abrikosov lattice exhibits still quasi long range translational order described by a non-universal exponent \bar\eta_{\bf G} which depends on the ratio of the renormalized elastic constants \kappa =\tilde c_{66}/\tilde c_{11} of the flux line (FL) lattice. Our calculations show clearly three distinct scaling regimes corresponding to the Larkin, the manifold and the asymptotic Bragg glass regime. On a wide range of intermediate length scales the FL displacement correlation function increases as a power law with twice of the manifold roughness exponent \zeta_{rm}(\kappa), which is also non-universal. Our results, in particular the \kappa-dependence of the exponents, are in variance with those of the variational treatment with replica symmetry breaking which allows in principle an experimental discrimination between the two approaches.