Scaling behavior of transport properties in one-dimensional network with both Rashba spin-orbit coupling and disorder

We study the transport properties of a one-dimensional (1D) quantum network with both Rashba spin-orbit coupling and geometric disorder. The 1D chain consists of a series of plaquettes with random sizes which are connected one by one at vertices. By calculating the average resistivity for varying lengths of the system, we show that there exists crossover from the delocalization to the step-like localization due to the interplay between the disorder and the spin-orbit coupling. In the step-like localization the scaling behavior is changed from metallic to insulating by increasing the system size. The size at which this change occurs depends on the strengths of the disorder. The results may shed light on the competition of the effects of disorder and spin-orbit coupling on the localization in 1D.