Electronic shot noise in fractal conductors
arXiv:0803.2709 · doi:10.1103/PhysRevLett.100.176804
Abstract
By solving a master equation in the Sierpinski lattice and in a planar random-resistor network, we determine the scaling with size L of the shot noise power P due to elastic scattering in a fractal conductor. We find a power-law scaling P ~ L^(d_f-2-alpha), with an exponent depending on the fractal dimension d_f and the anomalous diffusion exponent alpha. This is the same scaling as the time-averaged current I, which implies that the Fano factor F=P/2eI is scale independent. We obtain a value F=1/3 for anomalous diffusion that is the same as for normal diffusion, even if there is no smallest length scale below which the normal diffusion equation holds. The fact that F remains fixed at 1/3 as one crosses the percolation threshold in a random-resistor network may explain recent measurements of a doping-independent Fano factor in a graphene flake.
6 pages, 3 figures
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