Frequency-dependent response of pinned charge-density-wave condensates: Classical versus quantum description

Abstract

Frequency-dependent conductivity measurements are reported in the charge-density-wave state of ${\mathrm{Ta}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Nb}}_{\mathrm{x}}$ ${\mathrm{S}}_3$ alloys at microwave and millimeter-wave frequencies. For increasing impurity concentration, the pinning frequency of the charge-density-wave collective response increases sharply while the damping of the response remains constant. Although both the classical and quantum tunneling models describe the small-amplitude ac response of the pure materials for ω<${\mathrm{\omega }}_{\mathrm{p}}$, our results clearly support a classical oscillator response for ω>${\mathrm{\omega }}_{\mathrm{p}}$ and for the alloys.