Universal conductance fluctuations in Sierpinski carpets

Abstract

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.

Keywords

electronic transport / conductance fluctuation

References

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[40] It should be noted that the rms(G) in Figs. 3 and 4 seem not to be exactly same mainly due to discrete distribution of disorder strength W in numerical method. In order to reasonably describe the universal conductance fluctuations, we use a range of [–0.1, 0.1] (e²/h) based on the UCF value. The same method also used in other papers (Refs. [10–12]).

[41] In circular orthogonal ensemble, there does not exist a metal-insulator transition when system dimension below 3 according to the scaling theory of localization. Therefore, there is not UCF in circular orthogonal ensemble.

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