Collective modes in charge-density waves and long-range Coulomb interactions

We study theoretically the collective modes in charge-density waves in the presence of long-range Coulomb interaction. We find that earlier works by Takada and his collaborators are inadequate since they introduced inconsistent approximations in evaluating a variety of correlation functions. The amplitude mode is unaffected by the Coulomb interaction, while the phase mode splits into the phason with linear dispersion (i.e., acoustic mode) and the optical mode with an energy gap in the presence of the Coulomb interaction. In particular, we establish the temperature dependence of the phason velocity v_φ. A comparison with recent neutron-scattering data on the phason velocity in the charge-density wave of a single crystal of blue bronze K0.3{MoO}₃$ indicates that mean-field theory which includes the long-range Coulomb interaction gives an excellent description of the observed phason velocity.