A theory of the strongly pinned Fr�hlich mode

The extended Fukuyama-Lee-Rice theory of phase dynamics in quasi one-dimensional charge density wave systems is worked out for the pinned Frohlich mode in the strong pinning limit and for three spatial dimensions. The ac conductivity δ(ω) is expressed in terms of a self energy function Σ(ω) which is evaluated self consistently within the single sitet-matrix approximation. A case of hard momentum cut-off is shown to be inconsistent for reasons of analyticity breaking. A conserving theory for δ(ω) is worked out for a soft Lorentz cut-off and discussed in detail. Analytical results for the low frequency relaxation mode, for the “second dielectric constant”, for the high frequency pinned mode, and for the conductivity step at the frequency of the longitudinal optical phason are given in the descreened limit of low temperatures. The limit of very strong pinning is shown to be isomorphic to the case of the weakly pinned Frohlich mode ind=3, but with different parameters. Finally, a comparison is made between measurements of Re δ(ω) for two semiconducting charge density wave systems and the theories of both weak and strong pinning. The results are inconclusive with weak pinning slightly in favour over strong pinning.