Phase coherence in the current-carrying charge-density-wave state: ac-dc coupling experiments in NbSe3

Abstract

Various experiments which involve the joint application of dc and ac driving fields, $V=V_{\mathrm{dc}}+V_{\mathrm{ac}}cos\left(\omega t\right)$, are reported for the charge-density-wave (CDW) state of the linear-chain compound Nb${\mathrm{Se}}_3$. Steps are observed in the dc $I-V$ characteristics when ac driving fields are applied. The complex ac response ${\sigma }_{\mathrm{ac}}\left(\omega \right)$ is also strongly influenced by the application of dc fields, with sharp changes occurring in ${\sigma }_{\mathrm{ac}}\left(\omega \right)$ for well-defined driving frequencies and bias fields. These phenomena are the consequence of interference effects between the applied ac signal and the intrinsic current oscillations. In both cases, the ac "interference" frequency is proportional to the excess current $I_{\mathrm{CDW}}$ carried by the charge-density wave. We analyze our experiments in terms of a simple nonlinear equation proposed previously to account for the field- and frequency-dependent response and current oscillation phenomena. The equation is formally identical to the equation describing a resistively shunted Josephson junction (Stewart-McCumber model). Analysis in terms of this equation leads to a highly coherent sample response where the specimen can be described by a single degree of freedom. Our observations are also discussed in light of recent theories of CDW pinning and dynamics.