Disorder Driven Lock-In Transitions of CDWs and Related Structures

TL;DR

This paper investigates how frozen-in disorder influences lock-in transitions of charge density waves (CDWs) in low-dimensional systems, revealing disorder-driven phase transitions and non-universal decay behaviors.

Contribution

It introduces a theoretical framework for understanding disorder effects on lock-in transitions in CDWs, including critical exponents and phase diagrams in various dimensions.

Findings

Disorder induces strong fluctuation effects below four dimensions.

A disorder-driven continuous transition occurs for p > p_c=6/π in 3D.

Non-universal algebraic decay depends on elastic constants' Poisson ratio.

Abstract

Thermal fluctuations are known to play an important role in low-dimensional systems which may undergo incommensurate-commensurate or (for an accidentally commensurate wavevector) lock-in transitions. In particular, an intermediate floating phase with algebraically decaying correlations exists only in D=2 dimensions, whereas in higher dimensions most features of the phase diagram are mean-field like. Here we will show, that the introduction of frozen-in disorder leads to strong fluctuation effects even in D<4 dimensions. For commensurate wavevectors the lattice pinning potential dominates always over weak impurity pinning if p \le p_c=6/\pi (D=3), where p denotes the degeneracy of the commensurate phase. For larger p a disorder driven continuous transition between a long-range ordered locked-in phase and quasi-long-range ordered phase, dominated by impurity pinning, occurs. Critical exponents of this transition, which is characterized by a zero temperature fixed point, are calculated within an expansion in 4-D. The generalization to incommensurate wavevectors will be discussed. If the modulation in the quasi-long-range ordered phase has hexagonal symmetry, as e.g.for flux-line lattices, the algebraic decay is non-universal and depends on the Poisson ratio of the elastic constants. Weakly driven transport is dominated by thermally activated creep in both phases, but with different creep exponents.