Physica B 284}288 (2000) 1659}1660

Charge-density-wave sliding in ring-shaped crystals of NbSe
Y. Okajima*, H. Kawamoto, M. Shiobara, K. Matsuda, S. Tanda, K. Yamaya
Department of Applied Physics, Hokkaido University, Sapporo 060-8628, JapanAbstract
We report the "rst measurements of resistivity for a ring-shaped crystal of the quasi-one-dimensional conductor
NbSe . The temperature dependence of resistivity and current}voltage characteristics clearly demonstrate that the onedimensional chains are along the circumference of the ring and the charge-density wave (CDW) can slide along the ringabove a threshold "eld. The ring crystal is suitable for the investigation of interference phenomena in the CDW system.
We also "nd that the ring crystal cannot be regarded as two CDW conductors connected in parallel.  2000 Elsevier
Science B.V. All rights reserved.
Keywords: Charge-density wave; Interference phenomenon; Ring

There are many topics in the physics of one-dimensional metallic rings, especially in the case of mesoscopic
ones. The persistent current and the interference phenomena have been investigated experimentally and theoretically for a metal ring threaded by a magnetic #ux.
The charge-density wave (CDW) is a candidate which
may show such phenomena. Theoretical work is reported
on the CDW in a one-dimensional ring with electron}phonon interaction [1}6]. Recently, Latyshev et al.
investigated the CDW sliding through the columnar defects in magnetic "eld using the quasi-one-dimensional
conductor NbSe [7]. They claimed that their observa
tion was a manifestation of the Aharonov}Bohm e!ecton the sliding CDW. Single crystals of NbSe are usuallyobtained in a form of whisker-shape with the longest
direction along the one-dimensional axis. Quite recently,
we have successfully synthesized ring- and tube-shaped
crystals of NbSe with good reproducibility [8]. Here wereport the "rst measurements of resistivity in a ringshaped crystal of NbSe .
Crystals of NbSe were synthesized by reacting theelements in an evacuated quartz tube. We obtained several ring-shaped crystals from each of several batches.
Details of sample preparation are described elsewhere[8]. The diameter of the ring crystal used in the present* Corresponding author.
E-mail address: okajima@eng.hokudai.ac.jp (Y. Okajima)

study is &200 lm. For the resistivity measurements
gold wires with diameter of 10 lm were attached using
silver paste on the surface of the crystal. The arrangementof the electrical contacts is shown in the inset to Fig. 1.
For measurements of the current}voltage characteristics,
the voltages < and < across the voltage contacts were
measured as a function of total current I in the constantcurrent mode.
The temperature dependence of resistivity along thecircumference of the ring crystal was very similar to thatof the whisker crystals along the b-axis of NbSe , that is,the one-dimensional chains. The two increments due tothe CDW transitions were clearly observed just below
140 and 56 K, which are very close to the transition
temperatures in the whisker crystals. The resistivity at
300 K was very similar to that parallel to the b-axis of thewhisker crystals. In Fig. 1(a), the voltage < across the left
arm and d< /dI measured at ¹"44.5 K are plotted as
a function of the total current I. The voltage < showed
a nonlinear behavior due to the CDW sliding abovea threshold value of the total current I &1.8 mA. This is2
fairly clear in the d< /dI versus I plot. Similar behavior

was also observed for the voltage < across the right arm
and d< /dI around I &3.5 mA, as shown in Fig. 1(b).

2
The threshold "eld E for the nonlinear conduction is
2&320 mV/cm for the left arm and &285 mV/cm for theright arm, respectively. These values of E are similar to2that for the whisker crystals. The present results clearly
demonstrate that the ring crystal of NbSe has the same

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Y. Okajima et al. / Physica B 284}288 (2000) 1659}1660

comparable to the size of the present ring crystal. The
ring crystal is suitable for the investigation of the interference phenomena in the CDW system.
As observed in Fig. 1(b), there is a jump aroundIH&1.9 mA in d< /dI for the right arm. The value of thetotal current IH corresponds to the threshold value forthe nonlinear conduction of the left arm due to the CDWsliding. We also observed structures in d< /dI around 4.8

and 7.2 mA. A ring crystal might be considered as twoCDW conductors connected in parallel. From this pointof view, we have simulated the measurements phenomenologically. Results of the simulations showed that thejump at IH was due to decrease of the current #owing theright arm. However, d< /dI just above IH abruptly de
creased in the simulation, which di!ers from the measurements. The structures in d< /dI did not appear in thesimulation. These di!erences between the measurements
and the simulations indicate that the ring crystal cannot
be regarded as two CDW conductors connected in parallel. The origin of the di!erence should be ascribed to thering geometry of the present crystal.

Fig. 1. Voltages < and < developed across the left (a) and right(b) arms of the ring-shaped crystal plotted as a function of thetotal current through the ring. Current derivative of < and
< are also shown.
features as the whisker crystals and that the one-dimensional chains in the ring crystal are along the circumference of the ring. The coherence length of the CDW
velocity in NbSe is typically &100 lm [9], which is

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