Pinned and bound collective-mode state in charge-density-wave condensates

We have studied the complete electrodynamical response of the model charge-density-wave compounds ${\mathrm{K}}_{0.3}$ ${\mathrm{Mo}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{W}}_{\mathit{x}}$ ${\mathrm{O}}_3$ (x=0 and 0.015), (${\mathrm{TaSe}}_4$ ${)}_2$I and ${\mathrm{TaS}}_3$ by combining various optical experiments conducted in a broad spectral range. Our analysis leads to two distinct resonances in the dc to far-infrared (FIR) spectral range. We argue that the first resonance, at the so-called pinning frequency, is due to the oscillatory response of the collective mode and suggest that the FIR optical mode is due to a bound collective-mode resonance, analogous to bound phonon states in semiconductors. We discuss a simple phenomenological approach, based on a Clausius-Mossotti-type model, and evaluate the parameters that characterize the FIR mode.