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arXiv:cond-mat/9708116 · Physical Review Letters

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

Thorsten Emig A, Thomas Nattermann

Published Dec 22, 1997• 19 citations
arXivHTMLPDF

Abstract

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 $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3$ dimensions, we find for commensurate phases of order $p>{p}_{c}\ensuremath{\approx}6/\ensuremath{\pi}$ 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 $\ensuremath{\mu}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}p}^{2}{/p}_{c}^{2}\ensuremath{-}1$ and $\ensuremath{\epsilon}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4\ensuremath{-}d$ and fulfill the scaling relations of random field models. Implications for flux-line lattices in high temperature superconductors are briefly discussed.

DOI
10.1103/physrevlett.79.5090

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Randomly placed impurities that alter the local exchange couplings, but do not generate random fields or destroy the long-range order, roughen domain walls in Ising systems for dimensionality 53<d<5\frac{5}{3}<d<535​<d<5. They also pin (localize) the walls in energetically favorable positions. This drastically slows down the kinetics of ordering. The pinned domain wall is a new critical phenomenon governed by a zero-temperature fixed point. For d=2d=2d=2, the critical exponents for domain-wall pinning energies and roughness as a function of length scale are estimated from numerically generated ground states.
We study the effects of quenched disorder on the two-dimensional ddd-wave superconductors (SCs) at zero temperature by Monte Carlo simulations. The model is defined on the three-dimensional (3D) lattice and the SC pair field is put on each spatial link as motivated in the resonating-valence-bond theory of the high-Tc{T}_{c}Tc​ SCs. For the nonrandom case, the model exhibits a second-order phase transition to a SC state as density of charge carriers is increased. It belongs to the universality class different from that of the 3D XYXYXY model. Quenched disorders (impurities) are introduced both in the hopping amplitude and the plaquette term of pair fields. Then the second-order transition disappears at a critical concentration of quenched disorder, ${p}_{c}\ensuremath{\simeq}15%$. Implication of the results to cold atomic systems in optical lattices is also discussed.
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Spin-models in random fields (RFs) are good representations of many impure materials. Their macroscopic collective behaviour is dominated by the fluctuations in the random fields which accumulate on large scales even if the local field is arbitrarily small. This feature is shared by other weakly disordered models, like flux lines or domain walls in random media. We review some of the main theoretical attempts to describe such systems. A modification of Harris’ argument demonstrates that at the critical point the RF disorder is relevant and that (hyper)scaling must be changed. A domain argument invented by Imry and Ma shows that long-range order is not destroyed by weak RFs in more than d=2 dimensions. This result is supported both by a more refined treatment of the domain argument and by considering the roughness of an isolated domain wall due to the randomness. The wall (or flux line) becomes rough due to disorder but if d>2 the wall remains a well-defined object in RF systems. Different approaches are used to calculate the roughness exponent ζ for walls and lines. Some applications of ζ for the description of type-II superconductors and incommensurate systems are given. More detailed calculations are possible for one-dimensional, Bethe-lattice or the hierarchical Dyson model systems, which confirm as a rule the more approximate treatment of the other sections. In one dimension there is an interesting relation between the statistical mechanics of these models and nonlinear dynamics. Non-classical critical behaviour occurs in RF systems for d<6 and is determined in general by three independent exponents which fulfil certain inequalities. The new exponent θ≡yJ>0 is related to the violation of conventional hyperscaling and is determined by the energy ~H0ξ0 of a correlated region of size ξ. In a renormalization group treatment, the temperature T turns out to be a (dangerous) irrelevant variable which is the most prominent property of the systems considered in this review. The irrelevance of thermal fluctuations on large scales produces metastability and hysteresis effects both in the transition region and in the ordered phase, only briefly considered here. These features occur also in other systems with a disordered T=0 fixed point like in the ordered phase of a spin-glass.