Electronic shot noise in fractal conductors

TL;DR

This paper investigates how shot noise scales in fractal conductors, revealing a scale-independent Fano factor of 1/3 even with anomalous diffusion, which may explain doping-independent measurements in graphene.

Contribution

It provides a theoretical analysis of shot noise in fractal conductors using master equations, showing scale-invariant Fano factor and its implications for experimental observations.

Findings

Shot noise power scales as P ~ L^(d_f-2-alpha).

Fano factor remains at 1/3 regardless of diffusion type.

Results may explain doping-independent Fano factors in graphene.

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.