Elastic Properties of Charge-Density-Wave Conductors: ac-dc Electric Field Coupling

We have measured Young's modulus $Y$ and internal friction $\delta$ of the charge-density-wave (CDW) conductors Ta${\mathrm{S}}_3$ and Nb${\mathrm{Se}}_3$, in the presence of combined ac and dc electric fields. In the pinned CDW state, the elastic properties are sensitive to even small ac-field amplitudes. In the sliding-CDW state, sharp harmonic and subharmonic anomalies are observed in $Y$ and $\delta$; these coincide with Shapiro-type interference in the electronic response. Our experiments demonstrate that internal degrees of freedom (incoherence) of the CDW condensate are intimately tied to the dc- and ac-field-induced elastic anomalies.