Theory of quasi-one-dimensional conductors: Interaction between chains and impurity effects

A theory of impurity effects in quasi-one-dimensional conductors, such as KCP, is developed. Our approach takes into account phase fluctuations of the charge-density wave (CDW) and includes the effects of weak interchain interaction. The impurities are assumed to interact with the CDW mainly through forward scattering of electrons. Dynamical structure factors are calculated in various temperature limits. For the purely one-dimensional system with a Gaussian or Poisson distribution of impurity potentials the structure factor is calculated exactly. In addition to two phason branches, there is an impurity-induced central peak. The width in momentum is determined by impurities whereas the width in frequency is proportional to temperature. Corrections due to interchain coupling are included by means of a high-temperature expansion which also gives an estimate of $T_c$. At low temperatures the structure factor is calculated in the three-dimensional continuum approximation. There are phason branches, a highly anisotropic elastic peak determined by impurities, and a Bragg peak indicating that long-range order exists. The conditions for the continuum representation to be valid are estimated: It is shown that for large enough impurity concentration no long-range order can exist because of a melting of the "CDW lattice." We suggest that a spin-glass-like ordering may exist at low temperatures in KCP.