Combined investigation of collective amplitude and phase modes in a quasi-one-dimensional charge density wave system over a wide spectral range

We investigate experimentally both the amplitude and phase channels of the collective modes in the quasi-1D charge-density-wave (CDW) system, ${\mathrm{K}}_{0.3}{\mathrm{MoO}}_3$, by combining (i) optical impulsive-Raman pump-probe and (ii) terahertz (THz) time-domain spectroscopy, with high resolution and a detailed analysis of the full complex-valued spectra in both cases. This allows an unequivocal assignment of the observed bands to CDW modes across the THz range up to $9\mathrm{THz}$. We revise and extend a time-dependent Ginzburg-Landau model to account for the observed temperature dependence of the modes, where the combination of both amplitude and phase modes allows one to robustly determine the bare-phonon frequencies and electron-phonon (e-ph) coupling parameters. While the e-ph coupling is indeed strongest for the lowest-energy phonon, dropping sharply for the next higher frequency phonons, it grows back significantly for the higher-energy phonons, demonstrating their important role in driving the CDW formation. We also include a reassessment of our previous analysis of the lowest-lying phase modes. Assuming weaker electronic damping for the phase channel results in a qualitative picture more consistent with quantum-mechanical treatments of the collective modes, with a strongly coupled amplitudon and phason being the lowest frequency modes.