We measured the electrical conductivities of quasi-one-dimensional (Q1D) electron systems on liquid helium surface as a function of temperature between 0.04 and 1.7 K. We prepared two kinds of the Q1D system with different materials. In the first system, the electrons were confined in a one-dimensional geometry on a suspended surface of liquid helium within multi channel made over plastic optical fibers. In the second system, the electrons were similarly confined in a single narrow channel made over metallic electrodes. In both systems, the electrical conductivity increased first with decreasing temperature, and passing through a maximum started to decrease. The magnitude of the maximum for the second system was much smaller than that of the first one. The peak temperature was 0.8 K for the first system and 1.2 K for the second system. From these results, we could deduce that the electrons localize near the edge of the channel at low temperature. This localization was possibly connected to the surface roughness of the substrate suspending the helium surface.
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