Electric field depinning of charge density waves

The pinning of charge-density waves by impurities is considered in systems that exhibit at least short-range order in three dimensions. Impurities are classified into strong and weak with quite different pinning properties. The pinning of spin-density waves is weak and the phase values at impurity sites are almost random, in agreement with a recent experiment. The electric field required to depin the charge-density wave is estimated. The coupling between a drifting charge-density wave and carriers either from a remnant Fermi surface or thermal excitation is considered. Attention is focused on umklapp scattering of carriers by phasons as a coupling mechanism at finite temperature. The conductivity in the high-electric-field depinned limit can be large. Dislocations in the charge-density-wave lattice are examined with particular emphasis on the piecewise motion of the charge-density wave through the motion of dislocations. We also discuss the generation of dislocations by the analog of Frank-Read sources. The unusual nonlinear conductivity observed in Nb${\mathrm{Se}}_3$ is interpreted in terms of depinning of charge-density waves. The possibility of observing similar effects in other systems is briefly examined.