A THEORY OF THE WEAKLY PINNED FROHLICH MODE

Extending earlier work of Littlewood (1987) a theory for the collective mode ("Fröhlich mode") response of weakly pinned charge density waves (CDW) is given. Long range Coulomb interaction is incorporated in both a proper definition of the measured ac conductivity σCDW(ω) and in the Fukuyama-Lee-Rice treatment of phason dynamics. The frequency and wave number dependent quasi particle resistivity is shown to appear only in the internal phason lines in the perturbation expansion of the impurity averaged phason propagator Dren. Quantitative results for σCDW(ω) are evaluated within the self-consistent Born approximation to Dren in three spatial dimensions taking anisotropy into account. Besides the low frequency relaxation mode we find a significant effect of the longitudinal optical phason ωLO on the Fröhlich mode pinning frequency when descreening sets in at low temperatures. This is yet another manifestation of selection rule breaking by inhomogeneous pinning and establishes the special role that ωLO plays in the dynamics of CDW. An explicit analytical formula for σCDW(ω) is given and discussed in some detail including the important analyticity properties. Available measurements of the linear ac response in a wide range of frequencies and conductivities are compared with the theory and found to agree with the theoretical predictions supporting the concept of weak pinning in CDW. © 1990 Springer-Verlag.