Experimental Proof of Universal Conductance Fluctuation in Quasi-1D Epitaxial Bi$_{2}$Se$_{3}$ Wires

We report on conductance fluctuation in quasi-one-dimensional wires made of epitaxial Bi$_{2}$Se$_{3}$ thin film. We found that this type of fluctuation decreases as the wire length becomes longer and that the amplitude of the fluctuation is well scaled to the coherence, thermal diffusion, and wire lengths, as predicted by conventional universal conductance fluctuation (UCF) theory. Additionally, the amplitude of the fluctuation can be understood to be equivalent to the UCF amplitude of a system with strong spin-orbit interaction and no time-reversal symmetry. These results indicate that the conductance fluctuation in Bi$_{2}$Se$_{3}$ wires is explainable through UCF theory. This work is the first to verify the scaling relationship of UCF in a system with strong spin-orbit interaction.