A New Disorder-Driven Roughening Transition of Charge-Density Waves and Flux-Line Lattices

We study the competition between pinning of a charge-density wave by random distributed impurities and a periodic potential of the underlying crystal lattice. In $d=3\mathrm{}$ dimensions, we find for commensurate phases of order $p>\mathrm{}{p}_c\approx 6/\pi$ a disorder-driven continuous roughening transition from a “flat” phase with translational long-range order to a “rough” glassy phase with quasi-long-range order. Critical exponents are calculated in a double expansion in $\mu {=p}^2{/p}_c^2-1\mathrm{}$ and $\epsilon =4-d$ and fulfill the scaling relations of random field models. Implications for flux-line lattices in high temperature superconductors are briefly discussed.