Universal Conductance Fluctuation in Sierpinski Carpet

We report a theoretical investigation on conductance fluctuation of disordered two-terminal device in Sierpinski carpet. We find that the conductance fluctuation does not display a universal feature in circular orthogonal ensemble. But in the presence of magnetic field or spin-obit coupling, a universal conductance fluctuation (UCF) appears. More specify, in the presence of magnetic field, the UCF value is about 0.74 ± 0.01 (e2/h), while when applied spin-orbit coupling the UCF value exists also around 0.74 ± 0.01 (e2/h). By further investigating the conductance distribution in the critical disorder strength, we find that both of the symmetries share the same distribution function. Our work provide a better understanding of the transport properties of regular fractal structure and shed light on more transport studies of fractals.