Elastic Theory of pinned flux lattices

TL;DR

This paper investigates how weak impurity disorder pins flux lattices, revealing universal logarithmic displacement growth and algebraic order, using variational and renormalization group methods, with implications for experiments.

Contribution

It provides a detailed analysis of flux lattice pinning, demonstrating universal behavior and crossover phenomena using two complementary theoretical approaches.

Findings

Displacements grow logarithmically with distance in 2<d<4.

Algebraic quasi-long range translational order persists.

The crossover function between regimes is computed and experimentally observable.

Abstract

The pinning of flux lattices by weak impurity disorder is studied in the absence of free dislocations using both the gaussian variational method and, to $O(\epsilon=4-d)$, the functional renormalization group. We find universal logarithmic growth of displacements for $2<d<4$: $\overline{\langle u(x)-u(0) \rangle ^2}\sim A_d \log|x|$ and persistence of algebraic quasi-long range translational order. When the two methods can be compared they agree within $10\%$ on the value of $A_d$. We compute the function describing the crossover between the ``random manifold'' regime and the logarithmic regime. This crossover should be observable in present decoration experiments.