Collective modes in the charge-density wave state of K$_{0.3}$MoO$_3$: The role of long-range Coulomb interactions revisited

TL;DR

This paper investigates how long-range Coulomb interactions influence collective modes in the charge-density wave state of K$_{0.3}$MoO$_3$, revealing the protective role of phonons and matching experimental data with a multi-phonon model.

Contribution

It provides a detailed theoretical analysis of Coulomb effects on collective modes, highlighting the phonon protection of the phase mode and clarifying temperature-dependent behaviors.

Findings

Long-range Coulomb interactions do not gap the lowest phase mode due to phonon protection.

Amplitude fluctuations are unaffected by Coulomb interactions in Gaussian approximation.

Temperature dependence of mode energies largely explained by a multi-phonon Fröhlich model.

Abstract

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 K$_{0.3}$MoO$_3$. With the exception of the lowest phase mode, the temperature dependence of the measured mode energies can be quantitatively described within a multi-phonon Fr\"{o}hlich model for generic electron-phonon interactions neglecting long-range Coulomb interactions.