Universal conductance fluctuations in Sierpinski carpets

We theoretically investigate the conductance fluctuation of two-terminal device in Sierpinski carpets. We find that, for the circular orthogonal ensemble (COE), the conductance fluctuation does not display a universal feature; but for circular unitary ensemble (CUE) without time-reversal symmetry or circular symplectic ensemble (CSE) without spin-rotational symmetry, the conductance fluctuation can reach an identical universal value of 0.74±0.01(e²/h). We further find that the conductance distributions around the critical disorder strength for both CUE and CSE systems share the similar distribution forms. Our findings provide a better understanding of the electronic transport properties of the regular fractal structure.