Theory of Sound Wave and Phason in a Quasi-One-Dimensional Incommensurate CDW System. II. Acoustic Anomalies atTc

Anomalies of the sound velocity and ultrasonic attenuation coefficient at an incommensurate CDW transition temperature ( T c ) are investigated in a quasi-one-dimensional system. A scaling relation between the anomaly above T c and that below T c is established. The temperature dependence of the anomaly shows a cross-over from one to three dimensions according to a change of the dimensionality of critical fluctuations. The accoustic anomalies are shown to be enhanced by breaking of the charge conjugation symmetry resulting from the nonlinearity of the electron dispersion. As a result, the sound velocity shows a dip which diverges as f 3/2 (τ) for τ≫τ 1 and as (τ/τ 1 ) f 3/2 (τ) for \(τ{}τ₁\) where τ=|( T c - T )/ T c |, f n (τ)=τ - n and τ 1 is a non-dimensional cross-over temperature. The ultrasonic attenuation coefficient diverges at T c as f 5/2 (τ) for τ≫τ 1 and as (τ/τ 1 ) f 5/2 (τ) for \(τ{}τ₁\). For both anomalies, the scaling relation shows that f n (τ) above T c is transformed into 2 f n (2τ) below T c .