Collective modes in the charge density wave state of K0.3MoO3 : Role of long-range Coulomb interactions revisited

We re-examine the effect of long-range Coulomb interactions on the collective amplitude and phase modes in the incommensurate charge-density-wave ground state of quasi-one-dimensional conductors.Using an effective action approach we show that the longitudinal acoustic phonon protects the gapless linear dispersion of the lowest phase mode in the presence of long-range Coulomb interactions. Moreover, in Gaussian approximation, amplitude fluctuations are not affected by long-range Coulomb interactions. We also calculate the collective mode dispersions at finite temperatures and compare our results with the measured energies of amplitude and phase modes in ${\mathrm{K}}_0.3{\mathrm{MoO}}₃$. With the exception of the lowest phase mode, the temperature dependence of the measured mode energies can be quantitatively described within a multiphonon Fr\"ohlich model for generic electron-phonon interactions neglecting long-range Coulomb interactions.