Physica B 284}288 (2000) 1914}1915
Electrical conductivity of quasi-one-dimensional electrons on helium "lm Hideki Yayama *, Igor B. Berkutov, Akihisa Tomokiyo Department of Physics, Faculty of Science, Kyushu University, 4-2-1 Ropponmatsu, Fukuoka 810-8560, Japan Institute for Low Temperature Physics and Engineering, Academy of Sciences of Ukraine, Kharkov, Ukraine
Abstract Temperature dependence of electrical conductivity of quasi-one-dimensional (Q1D) electrons on helium "lm capillary-condensed in grooves of an optical di!raction grating was measured. The conductivity showed a maximum near 1.3 K and a minimum near 0.7 K. This result was quite di!erent from that of two-dimensional electron system and the theory for Q1D system presented so far. A qualitative explanation for the present result was given. 2000 Elsevier Science B.V. All rights reserved. Keywords: Electrical conductivity; Helium "lm; One-dimensional electron system
The Q1D electron system on liquid helium has been developed by some groups [1}4] and the investigation on the conductivity is in progress now. For this system, Sokolov et al.  presented a theory that the mobility increases with decreasing temperature till near 0.1 K. On the other hand, Yayama et al.  showed that the electrical conductivity decreases as the temperature is lowered down to 0.6 K. Thus, the theory and experiment give di!erent results, and the temperature dependence of the conductivity has not been understood yet. In this paper, we report the conductivity of Q1D electrons in the temperature range between 0.5 and 1.8 K and present a qualitative explanation for the experimental result. We used a glass optical-di!raction-grating to produce the Q1D channels. The grooves of the grating were "lled with super#uid helium under the action of capillary force. The microscopic surface geometry of the grating is the following. The distance between the adjacent groove centers is 5 lm, the width of the groove is 3.8 lm, the depth is 0.2 lm at the center, the cross-section of the groove shows a triangular shape. The electrodes located underneath the grating were used to measure the con-
* Corresponding author. E-mail address: [email protected]
ductivity of electrons in the direction along the grooves with a technique so-called Sommer}Tanner  method. Fig. 1 shows the measured temperature dependence of the conductivity. As the temperature is lowered, the conductivity increases till 1.3 K. This tendency is in accordance with the two-dimensional electron system on the bulk helium  and the theory by Sokolov et al. : i.e., the electrons are scattered by the He gas atoms. But, on the contrary, it decreases between 1.3 and 0.7 K, and starts increasing again below 0.7 K. This behavior between 1.3 and 0.7 K is quite di!erent from that of twodimensional electron system  and the theory  for Q1D system. In our system, the inter-electron distance is smaller than the width of the groove and hence a few electrons distribute over the width of the groove. In this sense, the system is not pure 1D but Q1D. The electrons in the center of the groove are expected to have a conductivity similar to the theory by Sokolov et al.  as schematically shown in Fig. 2, because the helium thickness is large and the image force from the grating is small. We must note that the e!ect of image force from the grating is not taken into account in the theory . In contrast, the electrons near the edge of the groove are captured by the random image force caused from the surface roughness of the grating because the helium thickness near the edge is small. For this reason, the electrons near the edge localize
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 3 0 1 4 - 8
H. Yayama et al. / Physica B 284}288 (2000) 1914}1915
Fig. 1. Measured electrical conductivity as a function of temperature. The driving frequency is 100 kHz. The distance between helium level and grating surface is 8 mm.
ing temperature from 1.3 to 0.7 K as schematically shown in Fig. 2. Since all the electrons near the edge localize at low temperatures, only the electrons in the center contribute to the conduction. Therefore, the conductivity increases again with decreasing temperature below 0.7 K in the similar manner as the theory by Sokolov et al. . The measured result is an overall conductivity represented by a superposition of the both conductivities of electrons in the center and near the edge of the groove. Thus, the temperature dependence of the conductivity is explained by the localization of carriers near the edge due to the potential irregularities caused by the surface roughness of the solid substrate. References
Fig. 2. Schematic drawing of the conductivity. The total conductivity is represented by the superposition of two contributions; electrons near the center and the edge of the groove.
due to the potential irregularities at low temperatures . As a result, the conductivity decreases with decreas-
 Yu.Z. Kovdrya, V.A. Nikolaenko, Fiz. Nizk. Temp. 18 (1992) 1278 [Sov. J. Low Temp. Phys. 18 (1992) 894].  O.I. Kirichek, Yu.P. Monarkha, Yu.Z. Kovdrya, V.N. Grigor'ev, Fiz. Nizk. Temp. 19 (1993) 458 [Low Temp. Phys. 19 (1993) 323].  A.M.C. Valkering, P.K.H. Sommerfeld, P.J. Richardson, R.W. van der Heijden, A.T.A.M. de Waele, Czech. J. Phys. 46 (1996) 321.  R.J.F. van Haren, G. Acres, P. Fozooni, A. Kristensen, M.J. Lea, P.J. Richardson, A.M.C. Valkering, R.W. van der Heijden, Physica B 249 (1998) 656.  S.S. Sokolov, G.-Q. Hai, N. Studart, Phys. Rev. B 51 (1995) 5977.  H. Yayama, A. Tomokiyo, O.I. Kirichek, I.B. Berkutov, Yu.Z. Kovdrya, Fiz. Nizk. Temp. 23 (1997) 1172 [Low Temp. Phys. 23 (1997) 878].  W.T. Sommer, D.J. Tanner, Phys. Rev. Lett. 27 (1971) 1345.  Y. Iye, J. Low Temp. Phys. 40 (1980) 441.