Journal of the Physical Society of Japan
Vol. 69, No. 4, April, 2000, pp. 1251-1252

Short Notes

Quantum Collective Dynamics
of Charge-Density Waves
in Quasi-One-Dimensional
Orthorhombic TaS3
Ken-ichi Matsuda, Satoshi Tanda, Masato Shiobara,
Yoshitoshi Okajima, Kazuhiko Yamaya
and Noriyuki Hatakenaka1
Department of Applied Physics, Hokkaido University,
Sapporo 060-8628
1 NTT Basic Research Laboratories, Atsugi,
Kanagawa 243-0198(Received December 24, 1999)
KEYWORDS: charge-density waves, o -TaS3 , macroscopic quantum tunneling, phase slip

For more than 20 years, several aspects of the dynamics of the broken symmetry ground state, called chargedensity waves1) (CDWs), have been widely explored.
One of the most interesting properties is the nonlinear
conduction associated with sliding CDWs. At relatively
high temperatures, the general properties of this nonlinearity have been investigated in detail,1) and the dynamics of CDWs are well described by the classical model,2-4)
in which CDWs are regarded as a classical deformableobject.
At low temperatures, however, the transport properties of CDWs are radically different from those at highertemperatures.5) At such temperatures, the quantum nature of CDWs becomes pronounced. Recently, ZaitsevZotov observed a temperature-independent nonlinear current of orthorhombic TaS3 (o-TaS3 ) crystals at low temperatures,6, 7) which indicates a quantum-mechanical effect in CDW systems. He also found that the currentvoltage (I-V ) curves can partly be fitted by a scaling
formI ∼ exp(−const./E β )(1)with the scaling factor β ∼ 2. Several theories havebeen proposed to explain his experimental results.8-12)
Although Zaitsev-Zotov’s results are beyond question,
there is room for discussion concerning the scaling factor. We have a different interpretation:13) the factor may
change as a function of external electric fields. In thispaper, we investigate nonlinear conduction of o-TaS3 at
low temperatures, in order to determine the scaling factor related to quantum nucleation processes leading to
CDW phase slips.
We have measured the nonlinear conductivity of pureo-TaS3 at various temperatures ranging down to 50 mK.
The samples were prepared using the chemical vaportransport method. Typical sample dimensions were
5 mm×10 µm×1 µm. Special care was taken to eliminate the Joule-heating effect; the samples were prepared on a sapphire substrate and installed directly on
a 3 He-4 He mixing chamber. The typical resistance ratio

R4.2K /R300K was ∼ 3×106 and the linear resistance wastypically ∼ 5 × 108 Ω at 4.2 K. The I-V characteristics
were measured by the two-probe configuration, whichis particularly suitable for high-resistance measurement.
Electrical contacts were prepared by evaporating gold(Au) in a vacuum. To ensure accurate high-resistancemeasurements, we used triaxial cables to reduce the effects of both noise coupling and leakage currents. The
noise level of our setup was ≤ 10−14 A. The shape of themeasured I-V curves was reproducible and independentof the direction of the voltage sweep.
Figure 1 shows I-V characteristics in the temperature
range of 50 mK–6 K. The dashed line represents ohmic
behavior. Above 4 K, an ohmic contribution was observed below the threshold electric field VT . When theelectric field exceeded VT , nonlinear current carried byCDWs became apparent. Qualitatively, this behavior
corresponds to conventional I-V curves.14) Upon lowering the temperature to 3 K, the ohmic contribution fell
below the resolution of the measurement and the weak
nonlinearity which develops below VT became more pronounced. Further reducing the temperature stopped thetemperature variation of current at the largest fields first,
and then at smaller fields.
Figure 2 shows the temperature dependence of thecurrent I(T ) measured at various electric fields. Above
1 K, I(T ) can be approximated by the activation low
I(T ) = I0 exp[−∆(E)/kB T ], where ∆(E) is an energy
barrier which is a function of the electric field E. Below
0.1 K, temperature variation of nonlinear current vanished and I(T → 0) approached a nonzero value depending on the electric field. This is attributed to a novel
type of collective transport, presumably due to macroscopic quantum tunneling.
Now let us explore novel features of nonlinear collectivetransport. Suppose that the I-V curve observed at 50mK
can be roughly approximated by the scaling form I =I0 exp[−(V0 /V )β ]. We transform this scaling form into¸·d(ln I)(2)
= (1 − β) log(V ) + log(βV0β )log −d(1/V )to determine the precise value of β. The inset in Fig. 3shows the plot of −d(ln I)/d(1/V ) vs V on log-log scale
for the limiting I-V curve. The straight lines represent
least-square fitting to the data. The slope P is related toβ by the relation P = 1 − β. Figure 3 clearly shows thatthe limiting I-V curve consist of two branches: It can be
fitted by I ∼ exp(−const./V β ) with β = 0.23 ± 0.03 forsmaller electric fields, while β = 0.31 ± 0.03 for larger
ones. These results are completely different from thoseby Zaitsev-Zotov. βs obtained in this study are clearlyless than 1.
Within the existing theoretical frameworks, scaling
factor β can be determined by the type of nucleation
processes. For instance, β = 2 for a homogeneous phaseslips based on vortex-ring creation,10) while β = 1 forvortex-pair creation.9) Anyhow β is an integer basically.
In contrast, our experimental results suggest that β bea fraction: β = 0.23 ± 0.03 ∼ 1/4 for smaller electricfields, while β = 0.31 ± 0.03 ∼ 1/3 for larger ones. Thisrequires new models for nonlinear conduction of CDWs

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Short Notes

Fig. 1. I-V characteristics of o-TaS3 in the temperature rangeof 50 mK–6 K. The dashed line corresponds to ohmic behavior.
The threshold field is indicated by the arrow.

Fig. 3. The bias dependence of the nonlinear current observed at50 mK. The dashed line is a scaling form I = I0 exp[−(V0 /V )β ]with β = 0.31, I0 = 1.23 × 10−4 A, V0 = 2.84 × 103 V. The
dashed-and-dotted line is the same form with β2 = 0.23, I0 =1.27 × 1011 A, and V0 = 1.14 × 107 V. The inset shows the plotof −d(ln I)/d(1/V ) vs V on a log-log scale.

I ∼ exp(−const./E β ): β = 0.23 ± 0.03 for smaller electric fields while β = 0.31 ± 0.03 for larger ones. These“fractional” βs are quite different from the integer βs inprevious studies. These results imply that quantum nucleation processes leading to phase slips differ from theexisting ones.
We are indebted to K. Inagaki and Y. Kasai for thepreliminary measurement. We would like to thank H.
Matsukawa and M. Yumoto for stimulating discussions.

Fig. 2. The temperature dependence of the current I(T ) measured at various electric fields.

at low temperatures. One can image that I-V curves canbe represented by the form I ∼ exp(−const./E 1/(d+1) )where d is an integer. This form is reminiscent of the expression for variable-range-hopping in electron conduction of disordered systems. In addition, if d is regarded
as a system dimension index, it seems that dimensionality changes from d = 3 (β = 1/4) to d = 2 (β = 1/3)
as the electric field increases. Further investigations forclarify our speculations should be done in the future.
In summary, we have found novel quantum-mechanicalfeatures of the nonlinear conduction of o-TaS3 at low
temperatures. There are two branches of I-V characteristics with different scaling factors β in the expression1) For reviews of CDWs, see G. Grüner: Rev. Mod. Phys.
60 (1988) 1129; C. Schlenker: Physics and Chemistry ofLow Dimensional Inorganic Conductors (Plenum, New York,1996); P. Monceau: Electronic Properties of Quasi-OneDimensional Materials (Reidel, Dordrecht, 1985).
2) H. Fukuyama and P. A. Lee: Phys. Rev. B 17 (1978) 535.
3) P. A. Lee and T. M. Rice: Phys. Rev. B 19 (1979) 3970.
4) H. Matsukawa: J. Phys. Soc. Jpn. 56 (1987) 1522; ibid. 57(1988) 3463.
5) M. E. Itkis, F. Ya Nad’ and P. Monceau: J. Phys.: Condens.
Matter 2 (1990) 8327.
6) S. V. Zaitsev-Zotov: Phys. Rev. Lett. 71 (1993) 605.
7) S. V. Zaitsev-Zotov, G. Remenyi and P. Monceau: Phys. Rev.
B 56 (1997) 6388.
8) J. Bardeen: Phys. Rev. B 39 (1989) 3528.
9) K. Maki: Phys. Rev. Lett. 39 (1977) 46.
10) Ji-Min Duan: Phys. Rev. B 48 (1993) 4860.
11) K. Maki: Phys. Lett. A 202 (1995) 313.
12) H. Matsukawa, H. Miyake, M. Yumoto and H. Fukuyama:Proc. of the Int. Workshop on ELECTRONIC CRYSTALS
1999, Journal de Physique IV 9 (1999) Pr. 10–161.
13) N. Hatakenaka, M. Shiobara, K.-i. Matsuda and S. Tanda:
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