Physica B 284}288 (2000) 1657}1658

Single-crystal rings of NbSe : a system for CDW interference?
S. Tanda*, H. Kawamoto, M. Shiobara, Y. Sakai, S. Yasuzuka, Y. Okajima,
K. Yamaya
Department of Applied Physics, Hokkaido University, Sapporo 060-8628, JapanAbstract
We have produced new ring- and tube-shaped crystals of NbSe and found reproducible synthesizing conditions. Wehave con"rmed that the ring is a single-phase NbSe crystal from X-ray di!raction, and that a charge-density wave
(CDW) transition takes place near 140 K by observing satellites of electron di!raction peaks. The position of the satellites
coincides with that of the conventional NbSe at the CDW transition. Non-linear conduction due to the CDW slidingis also observed in the ring crystals. The threshold "eld is similar to the conventional ribbon-shaped NbSe

crystals.  2000 Published by Elsevier Science B.V. All rights reserved.
Keywords: Charge-density wave; Quantum interference; Ring; Topology

Macroscopic and mesoscopic topological matter suchas a spherical and torus and Moebius strip have been thesubject of much theoretical and experimental work forthe sake of its wealthy physical phenomena. Persistentcurrent in a metal ring threaded by a magnetic #ux wasproposed theoretically and observed experimentally [1].
Interference phenomena of electrons have also been
investigated for a metal ring; the Aharonov}Bohm (AB)
e!ect for thin gold rings [2] and the Altshuler}
Aronov}Spivak (AAS) e!ect for tube-like Mg "lms in
the weakly localized regime [3,4] and AAS-like e!ectfor NbSe with columnar defects [5]. Persistentcurrent and interference phenomena can also be observed for the electronic condensate in superconductorsof ring or tube shape. Can the persistent current exist also
in ring- and tube-shaped charge-density wave (CDW)systems?
In order to observe those e!ects, it is necessary toobtain an ideal ring-shaped sample of a one-dimensional(1D) material, such as organic-conductors or CDWNbSe of MX group systems. We have made ring- and

* Corresponding author.
E-mail address: tanda@eng.hokudai.ac.jp (S. Tanda)

tube-shaped crystals of NbSe , and found reproducible
synthesizing conditions.
The samples were prepared by the chemical vapor
transportation method. Single crystals of ring NbSe
were grown by using a solidi"cation technique. Thisemploys a stationary closed quartz tube inside a box
furnace. Starting materials were composed of a mixtureof bulk Se and Nb. The purity of all materials used in thiswork was 99.999%. The mixture was reacted at 7403C forthree weeks in situ quartz tube and then cooled to 2403C
at which temperature the oven was shut o!. Fig. 1 isFig. 1. Ring-shaped crystal of NbSe . Diameter of the ring is100 lm.

0921-4526/00/$ - see front matter  2000 Published by Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 8 1 6 - 1

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S. Tanda et al. / Physica B 284}288 (2000) 1657}1658

Fig. 3. Temperature dependence of resistivity of the ring-shapedcrystal along the circumference of NbSe .
Fig. 2. Satellites of CDW of ring-NbSe by electron di!raction
at 138 K, which is below the CDW transition temperature ¹ .
Q (0 0.24 0) is the wave vector of the CDW, bH the reciprocal
lattice vector.

an optical microscope picture of a typical ring-shaped
crystal of NbSe .
We ground up the samples of ring-shaped crystals inorder to identify composition and crystal structure. The
powder of the ring-shaped crystals shows a monoclinic
NbSe single phase by the measurements of the X-ray
di!raction methods. We found the ring-shaped crystal is
not a Nb Se , Nb Se , NbSe , Nb Se or other binary   compounds of Nb and Se. Lattice constants werea"10.01 As , b"3.48As , c"15.63 As , b"108.53, respectively. The ring-shaped samples were con"rmed to be
single crystals of NbSe .
Next, we performed electron-di!raction measurementof the ring-shaped NbSe at 138 K (less than ¹ , see
below). Fig. 2 shows satellites due to the CDW wave
vector of the ring-shaped NbSe crystals. The CDW
wave vector Q is (0 0.24$0.01 0), determined from theposition of the satellites di!racted by superlattice re#ection. The position of the satellites coincides with that of
the conventional NbSe at the CDW transition. Wecon"rmed that a CDW transition takes place in this ringof NbSe near 140 K. The CDW transition was also
con"rmed by the temperature dependence of the resistivity of a ring-shaped NbSe (Fig. 3). For this crystal, theusual four-probe method was used. There are two resistivity anomalies both along the a- and c-axis, as inprevious reports of temperature dependence of resistivity.
They are caused by the CDW transitions at 145 K (¹ )and 54 K (¹ ).
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