text: Linear chain compounds exhibiting CDW transport have CDW wavelengths λ = π/k incommensurate with (i.e., not an integer multiple of) the lattice constant. In such materials, pinning is due to impurities that break the translational symmetry of the CDW with respect to φ. The simplest model treats the pinning as a sine-Gordon potential of the form u(φ) = u[1 – cosφ], while the electric field tilts the periodic pinning potential until the phase can slide over the barrier above the classical depinning field. Known as the overdamped oscillator model, since it also models the damped CDW response to oscillatory (AC) electric fields, this picture accounts for the scaling of the narrow-band noise with CDW current above threshold.
  However, since impurities are randomly distributed throughout the crystal, a more realistic picture must allow for variations in optimum CDW phase φ with position – essentially a modified sine-Gordon picture with a disordered washboard potential. This is done in the Fukuyama-Lee-Rice (FLR) model, in which the CDW minimizes its total energy by optimizing both the elastic strain energy due to spatial gradients in φ and the pinning energy. Two limits that emerge from FLR include weak pinning, typically from isoelectronic impurities, where the optimum phase is spread over many impurities and the depinning field scales as n (n being the impurity concentration) and strong pinning, where each impurity is strong enough to pin the CDW phase and the depinning field scales linearly with n. Variations of this theme include numerical simulations that incorporate random distributions of impurities (random pinning model).