By solving a master equation in the Sierpinski lattice and in a planarrandom-resistor network, we determine the scaling with size L of the shot noisepower P due to elastic scattering in a fractal conductor. We find a power-lawscaling P ~ L^(d_f-2-alpha), with an exponent depending on the fractaldimension d_f and the anomalous diffusion exponent alpha. This is the samescaling as the time-averaged current I, which implies that the Fano factorF=P/2eI is scale independent. We obtain a value F=1/3 for anomalous diffusionthat is the same as for normal diffusion, even if there is no smallest lengthscale below which the normal diffusion equation holds. The fact that F remainsfixed at 1/3 as one crosses the percolation threshold in a random-resistornetwork may explain recent measurements of a doping-independent Fano factor ina graphene flake.
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机译：通过求解Sierpinski晶格和平面随机电阻网络中的主方程，我们确定了由于分形导体中的弹性散射而导致的散粒噪声功率P随大小L的变化。我们发现幂律定标P〜L ^（d_f-2-alpha），其指数取决于分形维数d_f和反常扩散指数α。这与时间平均电流I的比例相同，这意味着Fano因子F = P / 2eI与比例无关。即使不存在法线扩散方程式以下的最小长度尺度，我们也可以得到与正常扩散相同的F = 1/3值。当F越过随机电阻网络中的渗滤阈值时，F保持固定在1/3的事实可能解释了石墨烯薄片中与掺杂无关的Fano因子的最新测量。
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