Neutron-scattering investigations of the Kohn anomaly and of the phase and amplitude charge-density-wave excitations of the blue bronze ${\mathrm{K}}_{0.3}$${\mathrm{MoO}}_3$

The quasi-one-dimensional (1D) conductor ${\mathrm{K}}_{0.3}$${\mathrm{MoO}}_3$ undergoes a Peierls transition at ${\mathit{T}}_{\mathit{c}}$=183 K. Using cold-neutron scattering, we have succeeded in resolving in frequency and for wave vectors parallel to the chain direction the pretransitional dynamics and the collective excitations of the phase and of the amplitude of the charge-density-wave (CDW) modulation below ${\mathit{T}}_{\mathit{c}}$. The pretransitional dynamics consists of the softening of a Kohn anomaly at the wave vector 2${\mathit{k}}_{\mathit{F}}$ together with the critical growth of a central peak in the vicinity of ${\mathit{T}}_{\mathit{c}}$. In addition we observed just above ${\mathit{T}}_{\mathit{c}}$ the beginning of a decoupling between the fluctuations of the phase and of the amplitude of the CDW. These features are discussed within the framework of recent model calculations of the dynamics of the Peierls chain. The amplitude mode is clearly observed below ${\mathit{T}}_{\mathit{c}}$ with a quasiharmonic frequency ${\nu }_{\mathit{A}}$ and a damping ${\mathrm{{\rm Y}}}_{\mathit{A}}$, which perfectly agree with that found in a previous Raman scattering investigation of blue bronze. By continuity with the behavior of the pretransitional fluctuations, ${\nu }_{\mathit{A}}$ does not soften at ${\mathit{T}}_{\mathit{c}}$. The dispersion of the phase mode has also been measured in the chain direction near ${\mathit{T}}_{\mathit{c}}$. In this temperature range the phason velocity is quite high (about one-tenth of the Fermi velocity), giving a CDW mass enhancement of ∼100. High-resolution measurements show that the phason response is overdamped at 2${\mathit{k}}_{\mathit{F}}$ with a small gap whose estimated value corroborates that recently found for the high-frequency pinning mode of the blue bronze by millimeter-wavelength-range conductivity measurements.