It is proposed that ac voltage (^a c ) oscillations observed in sliding charge-density-wave systems are caused by phase vortices at the sample ends. The model's prediction that v ac is length independent is verified experimentally. The long-range phase coherence implied by thermal-gradient experiments is consistent with the vortex model but not with models based on impurities.PACS numbers: 72.15.Nj, 72.20.Ht,One of the most puzzling features of electronic transport in the series of compounds that demonstrate charge-density-wave (CDW) conduction is the appearance of well defined voltage oscillations 1 when the dc electric field exceeds a threshold value E T . The fundamental frequency of this oscillation has been shown 2 to be proportional to the current carried by the moving CDW. This phenomenon has been seen 3 in NbSe 3 , TaS 3 , (TaSe 4 ) 2 I, (NbSe 4 ) 10 / 3 I, and the bronzes K 0 . 3 MoO 3 and Rb 0 . 3 MoO 3 , all of which display nonlinear I-V curves associated with CDW depinning. Most of the theories 4 ' 6 proposed for the ac voltage invoke the impurities as the source of the current oscillations through their interaction with the moving CDW. The simplest such model is the impurity washboard model of Gruner, Zawadowski, and Chaikin. 4 In the static situation the weakly pinned condensate distorts its phase to maximize the pinning energy gained from the impurities. The average length of the domains within which the phase is roughly uniform is the Fukuyama-Lee-Rice (FLR) 7 length X FLR (10-50 Mm in NbSe 3 ). It is well established experimentally that the threshold field is determined by the impurity concentration. However, the situation when the CDW moves is less clear. In particular we shall present evidence showing that the phase coherence length (when sliding) is much longer than A FLR and infer that the impurities play no major role in the (narrow-band) noise generation. (A perplexing problem with domain structures in the sliding CDW is the question of how oscillations in adjacent domains couple to provide the sharp spectra seen. Also the question of what happens at walls separating domains with different velocities is unresolved.)We propose a model for the CDW noise based on the following assumptions: (I) An array of vortices is created when the CDW phase undergoes an abrupt change such as at the sample ends. (II) Regardless of the phase configuration in the static (pinned) condensate, when sliding occurs the phase coherence may extend over macroscopic distances approaching the sample length in pure samples. The creation and annihilation of the phase vortices at the sample ends leads to a modulation of the current which is observed as the ac noise. Various theories 8 ' 9 have explored the effect of internal degrees on the dynamics of the moving CDW. In our model we may regard the conduction noise as a manifestation of the internal degrees of freedom expressed as phase dislocations in inhomogeneous situations. The vortex array insofar as it is an energetically favorable way for the system to overcome ph...

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%'e have measured the complex dielectric constant of TaS3 and NbS3 at 9.8 GHz. In the chargedensity-wave state the conductivity at this frequency is several orders of magnitude larger than the dc value. The dielectric constant is of the order of 10 in both systems. Using the overdampedoscillator model, we calculate the temperature dependence of the crossover frequency as well as obtain estimates of the damping frequency and effective mass in TaS3.Some members of the linear-chain trichalcogenide family MX3 (where M =Nb, Ta and X=S,Se) display very unusual transport properties associated with the excitation of many-body modes in the charge-density-wave (CDW) state. The most well-known example' is NbSe3. Recently, TaS3 has become the subject of great interest following the work of Thompson et al, , who showed that TaS3 has anomalous transport properties similar to those of NbSe3. These include the existence of narrow-band noise, and a threshold field Ez-for non-Ohmic conduction.The microwave conductivity was also shown to be enhanced over the dc by Verma and co-workers and by Jackson et al.Predating the recent work on TaS3, Sambongi and coworkers ' had reported observing non-Ohmic dc conductivity in this compound.They interpreted the nonOhmicity as due to solitons. Roucau et al. discovered that TaS3 grows in two polytypes, viz. , the orthorhombic and monoclinic. The resistivity-versus-temperature (Rvs-T) profile shows two phase transitions in the rnonoclinic crystal as opposed to the orthorhombic, which shows only one. The experiments which showed behavior in TaS3 similar to that of NbSe3 were performed on the orthorhombic polytype. The experiments on TaS3 to be reported here are on the orthorhombic phase as well. We have also succeeded in observing narrow-band conduction noise in these orthorhombic samples, in agreement with the earlier results of Gruner et al. The observation of these anomalous transport properties in a compound that presumably has a commensurate CDW (Ref. 6) poses serious theoretical difficulties for the canonical model of CD% depinning. Therefore, more experimental work on TaS3 is highly desirable. A preliminary report of our microwave work appeared in Ref. 4. Here we provide a detailed report of the experiments together with some new analysis.Our samples of TaS3 were grown at 750'C in a 2-in. quartz tube for 4 weeks. In appearance, the crystals resemble grey whiskers. The longest samples have lengths exceeding 8 cm, but the widths rarely exceed 30 p. Because of the high growth temperature and the R-vs-T profile we conclude that these samples are orthorhombic. Monoclinic crystals were grown in a subsequent batch at 450'C for a period of 4 months. These crystals, which are thicker and resemble dendritic structures, show an Rvs-T profile quite distinct from the orthorhombic ones.No microwave studies were carried out on the monoclinic crystals as yet. The NbS3 samples were also grown at high temperature (700 C) by direct reaction of stoichiometric proportions to the elements. Yield was poorer than...

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