Scattering and transport properties of tight-binding random networks

We study numerically scattering and transport statistical properties of tight-binding random networks characterized by the number of nodes $N$ and the average connectivity $α$. We use a scattering approach to electronic transport and concentrate on the case of a small number of single-channel attached leads. We observe a smooth crossover from insulating to metallic behavior in the average scattering matrix elements $\bra |S_{mn}|^2 \ket$, the conductance probability distribution $w(T)$, the average conductance $\bra T \ket$, the shot noise power $P$, and the elastic enhancement factor $F$ by varying $α$ from small ($α\to 0$) to large ($α\to 1$) values. We also show that all these quantities are invariant for fixed $ξ=αN$. Moreover, we proposes a heuristic and universal relation between $\bra |S_{mn}|^2 \ket$, $\bra T \ket$, and $P$ and the disorder parameter $ξ$.

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