Theory of Sound Wave and Phason in a Quasi One-Dimensional Incommensurate CDW System I. –Long-Range Coulnmb Effect–

A microscopic theory of phason and sound wave is developed in a quasi one dimensional incommensulate CDW system within RPA. We prove a sum rule at finite temperatures, which means that a sum of screening due to the phason and that due to the quasiparticle excitations gives the same screening effect as that in a normal state. It leads to the same velocity of the sound wave as that in a normal state. Effects of quasi-particle screening on the dispersion of the phason are examined. As a consequence a singular behaviour is shown to result from velocities of thermally excited quasi-particles being too small to screen the induced charge of the phason near 0 K. The acoustic mode exists only above across-over temperature T 2 besides an optic mode corresponding to the Goldstone mode which exists below T c . This feature is similar to a superconductor in which the existence of the acoustic mode is well established both theoretically and experimentally.