PERGAMON

Solid State Communications 113 (2000) 451–454
www.elsevier.com/locate/ssc

Possibility of dynamic transitions in sliding charge-density waves
K.-i. Matsuda*, S. Tanda
Department of Applied Physics, Hokkaido University, N13W8 Kita-ku, Sapporo 060-8628, Japan
Received 9 August 1999; received in revised form 27 October 1999; accepted 28 October 1999 by H. Akai

Abstract
The transport properties of charge-density waves have been studied in orthorhombic TaS3 as a function of the electric field. In
the sliding state, we found that the power of the fundamental component of narrow-band noise has a minimum value at a bias
voltage Vc. Moreover, the field dependence of the non-linear current carried by CDW changes abruptly at Vc. These results
suggest the existence of a dynamic phase transition between plastic-flow phase and fluid-solid phase. q 2000 Elsevier Science
Ltd. All rights reserved.
Keywords: A. Disordered systems; D. Noise

1. Introduction
The influence of randomly quenched impurities on thedynamics of driven interacting systems has been the subjectof intense study. One area of particular interest has been thedynamics of disordered periodic systems, such as vortex
lattices in the type II superconductors [1], Wigner crystals[2], Josephson junction arrays [3] and charge-density waves(CDWs) [4–7].
In the last case, below the CDW transition temperature
TCDW, electronic density is spatially modulated along thechain direction. In the absence of pinning due to impurities
and lattice defects, CDWs have spatial long-range order andare free to slide. However, it has been argued that impurities
destroy the spatial long-range order and pin the system. The
dynamic properties of this system with quenched impurities
have a close relation to crystal growth phenomena [8]described by the Karder–Parisi–Zhang (KPZ) equation [9]and lead to very rich physics.
In recent theoretical studies [10,11], the existence of three
dynamical phases has been predicted as a function of external driving force V provided by an electric field. The firstregime is a pinned phase. For small V, the impurities pin
CDWs and destroy their spatial long-range order. When thedriving force exceeds a threshold driving force VT, CDWs
can de-pin and become mobile. The second regime VT ,V is a plastic-flow phase. In this regime, the motion of* Corresponding author.

CDWs is highly non-uniform. For V far higher than
VT VT ! V; a dynamical phase transition occurs andCDWs moves into the third regime: fluid–solid phase. In
this regime, despite the absence of true spatial long-rangeorder and periodicity, CDWs have long-range temporalcorrelation.
The de-pinning transition between the pinned phase andthe plastic-flow phase has already been studied and is fairlywell understood [12,13]. In contrast, the dynamic phasetransition between the plastic-flow phase and the fluidsolid phase has only recently begun to receive some attention and the existence of this transition has not yet been
examined in CDWs experimentally.
In this paper, we report the experimental evidence of theexistence of a dynamic phase transition in sliding CDWs. In
the sliding states, the power of the fundamental componentof the narrow-band noise (NBN) depends strongly on thebias voltage V and shows a minimum at a certain voltage Vc.
The field dependence of the CDW current also changes atthe same voltage Vc. The results indicate the existence ofthree phases in CDWs as a function of external driving
force: the pinned phase V , VT ; the plastic-flow phase
VT , V , Vc ; and the fluid-solid phase Vc , V:

2. Experimental
The orthorhombic TaS3 (o-TaS3) crystals analyzed in thisstudy were prepared using the chemical vapor method.

0038-1098/00/$ - see front matter q 2000 Elsevier Science Ltd. All rights reserved.
PII: S0038-109 8(99)00509-8

452K.-i. Matsuda, S. Tanda / Solid State Communications 113 (2000) 451–454

Fig. 1. Scaling plot of ICDW obtained from the I–V curves in o-TaS3
at 77.3 K. The crossover exponent obtained from the solid-line isz  1:1 ^ 0:1: VT  34:5 mV for this sample. ICDW increases
rapidly above Vc . 64:5 mV:

Powder X-ray diffraction showed an orthorhombic phase forthese crystals. We analyzed samples from the same preparation batch. Typical crystal dimensions were 1 mm ×10 mm × 1 mm; of which the longest dimension corresponds
to the chain axis. The sample was placed on a glass substrateand electrical contacts were produced by evaporating gold
in a vacuum. The length of each inter-contact arm wasapproximately 0.5 mm. The CDW transition temperature
TCDW is 214 K. The linear sample resistance was typically
1 kV at 77.3 K. We measured current–voltage characteristics and NBN in several samples. The current–voltage characteristics were measured using a four-probe configuration
and a DC voltage-control technique. We assume that I–Vcharacteristics are described in terms of two-fluid model. In
that case, the total current I can be written as I  In 1 ICDW ;where In is an ohmic component. Thus, the CDW current iscalculated as ICDW  I 2 V=Rn ; where Rn is the resistanceobserved below the threshold voltage VT.
The NBN measurements were carried out under fixedcurrent condition. The main difficulty in performing thesemeasurements was recording the small NBN signal of thesample. To solve this problem, we used a specially designed
cryostat and an ultra-low-noise amplifier with a gain of1000. A short cable was used between the sample and theamplifier to eliminate reflections and the effects of standingwaves. The signal was fed to a digital spectrum analyzer andeach spectrum was obtained by averaging 8192 sweeps.

3. Result and discussion
Fig. 1 shows the bias dependence of the CDW current

Fig. 2. The bias dependence of the spectrum of NBN in o-TaS3 at
T  77:3 K: The vertical axis represents the power of NBN in theunit of V 2 =Hz: Each section shows the shape of fundamental NBN ateach bias voltage. The width of fundamental NBN is normalized by
the half-power band width Df and the horizontal axis represents f~;
defined as f~  f 2 fNBN =Df : The parameters for each window are(a) V  52:52 mV; fNBN  405 Hz; Df  97:55 Hz; (b) 55.9 mV,875 Hz, 96.30 Hz; (c) 60.45 mV, 2150 Hz, 133.75 Hz; (d)65.98 mV, 4700 Hz, 340.60 Hz; (e) 73.26 mV, 10625 Hz,469.40 Hz; (f) 83.97 mV, 24125 Hz, 685.70 Hz; and (g)94.07 mV, 40375 Hz, 733.75 H, respectively.

ICDW above the threshold voltage VT. The horizontal axis
represents the reduced bias voltage V 2 VT =VT : For thissample, VT is 34.5 mV. The solid line indicates the following power law form ICDW , V 2 VT 1:1^0:1 : This result
seems to consistent with the theoretical prediction of depinning transition [12,13]. But recent theoretical [14] andexperimental [15,16] work have shown that experimental
systems are sufficiently small so that finite size effects
make the critical regime unobservable. Thus the scaling
behavior observed near VT probably indicates crossover
regime.
While the bias dependence of the CDW current near VT
obeys a scaling law, the ICDW –V curve bends at a field
marked Vc and ICDW increases abruptly for bias voltages
above Vc. For this sample, Vc , 64:5 mV: This remarkableincrease of ICDW implies that there is a different type ofsliding state above Vc.
It is generally accepted that normal carriers play animportant role in the dynamics of collective mode [26].
The uncondensate electrons screen the extra charge resulting from the CDW deformation, which is suppressed if theyare absent. In fact, unusual I–V characteristics have alreadybeen observed in some CDW materials (NbSe3 [17],K0.3MoO3 [18]) at low temperature. They are discussed inrelation with the vanishing screening effects in that temperature range. However, the bend in Fig. 1 is not caused by

K.-i. Matsuda, S. Tanda / Solid State Communications 113 (2000) 451–454

Fig. 3. The bias dependence of S fNBN  at T 
77:3 K: The verticalpaxis represents S fNBN  in the unit of dB V= Hz ; 10log V2 =Hz:S fNBN  increases slowly above Vc. S fNBN  is a minimum at Vc 
64:5 mV for this sample, and increases with decreasing bias voltage
below Vc.

screening effect since the motion of CDWs in the vicinity ofVc is much slower than the relaxation time of screening
effect due to uncondensed electrons.
To get other information about the dynamics of CDWs,
we measured the voltage fluctuation generated by sliding
CDWs. In particular, the NBN reveals spatio-temporalorder in CDWs. Thus, we investigated the power, S fNBN ;
and the fundamental frequency of NBN, fNBN, as a functionof the applied bias voltage. Fig. 2 shows the shapes of thefundamental component of the NBN for various values ofFig. 4. The relationship between fNBN and ICDW. Above Vc, ICDW isproportional to fNBN; however, below Vc, fNBN is not proportional toICDW.

453Fig. 5. Phase diagram in the DC-bias–temperature plane. The
hatched region indicates the pinned state. Both solid and dashedlines are guides to the eyes for the experimental data.

applied electric voltage at 77.3 K. This measurement wasactually performed under almost fixed current condition.
Thus, V represents the time-averaged DC value. The horizontal axis of each window represents a reduced frequency
defined as f~  f 2 fNBN =Df ; where Df is a half-power
bandwidth.
While both broad-band noise (BBN) and NBN wereobserved for voltages below Vc (2a–c), strong and sharp
NBN was observed above Vc (2e–g). As the bias voltage
increases, fNBN moves into a higher frequency. However, thepower of the NBN, S fNBN ; decreases significantly in therange VT , V , Vc  and shows a minimum in the vicinityof Vc (Fig. 2d).
The bias dependence of the power of the NBN is shown inFig. 3. As the bias voltage increases in the range VT , V ,Vc ; the power of NBN, S fNBN ; decreases significantly. On
the other hand, above Vc, S fNBN  increases slowly with thebias voltage. The bias dependence of the NBN observed
above Vc is similar to that of the conventional NBN inCDWs [19–22] and was qualitatively described by the classical model [23–25] which treats CDW as a classicaldeformable object and does not allow the plastic motion.
The bias dependence of S fNBN  below Vc is not reported
in previous experimental works. These results indicate that
there are two regions in the sliding state as function ofapplied bias voltage.
In a recent theoretical study [10], the existence of a dynamical phase transition between the plastic-flow phase andthe fluid-solid phase has been predicted. According to thetheoretical prediction, below critical bias voltage V p, themotion of CDWs is highly non-homogeneous. CDWs
recover spatio-temporal order above V p. The evidence ofsuch a phase transition is a scaling behavior of S fNBN ,uV 2 V p uf near V p, where f is a dynamical critical exponent. As shown in Fig. 3, The power of the NBN, S fNBN ;

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K.-i. Matsuda, S. Tanda / Solid State Communications 113 (2000) 451–454

shows a minimum in the vicinity of Vc. This result supports
the theoretical prediction.
If there are two different flow phases in the sliding state,another experimental evidence is expected in the relationship between ICDW and fNBN. Fig. 4 shows the relationshipbetween the fundamental frequency of the NBN, fNBN andthe CDW current ICDW at 77.3 K. The dashed line shown inFig. 4 represents a linear relationship. The bias voltage Vc
marked in both Figs. 1 and 3 approximately corresponds tofNBN . 5 kHz: Above fNBN $ 5 kHz; ICDW is approximately
proportional to fNBN. However, below fNBN # 5 kHz; ICDW isnot proportional to fNBN. This result indicates that thenumber of electrons carried by CDW changes as a functionof bias voltage below ,5 kHz.
In the temperature range 60 , T , 100 K; well-defined
VT and Vc are observed. Fig. 5 shows the phase diagram in
the DC-bias–temperature plane. The hatched region indicates the pinned state. We have used a solid line as a boundary between the pinned state and the plastic-flow phase, anddashed line as a boundary between the plastic-flow phaseand the fluid-solid phase. Both VT and Vc decrease withincreasing temperature.
4. Summary
The transport properties of charge-density waves (CDWs)
in orthorhombic TaS3 (o-TaS3) have been studied as a function of the electric field at 77.3 K. In the sliding state, we
found that the power of the fundamental component of theNBN shows a minimum at a bias voltage Vc. Moreover, thefield dependence of the non-linear current carried by CDW(ICDW) changes abruptly at Vc. Although it is difficult toevaluate the critical exponent f from the present available
data, these results indicate the existence of a dynamicalphase transition between the plastic-flow phase and thefluid-solid phase.
Acknowledgements
We would like to thank Prof K. Yamaya, Dr N.
Hatakenaka, Prof Y. Okajima and Prof T. Sambongi for

their useful discussion. This study was supported in partby a grant from the Japan Society for the Promotion ofScience for Young Scientists.

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