Quantum percolation in electronic transport of metal-insulator systems: numerical studies of conductance

The quantum site-percolation problem defined by a tight-binding one-electron Hamiltonian on regular simple cubic lattice with binary probability distribution of site energies P(ϵn) = pσ(ϵn) + (1 − p)σ(ϵn − ∞) is studied using the Landauer-Büttiker formalism and Green's function method. The dimensionless conductance g according to Landauer-Büttiker formula is calculated for a finite system of size L × L × L. The arithmetic and geometric (e〈lng〉) averages of g over many realizations of the disordered system are calculated. Plotting g for different L as a function of concentration p has enabled to find a critical p = pq such that g decreases (exponentially) with L for p < pq and it increases (linearly) with L when p > pq. Thus, we have demonstrated the Anderson metal-insulator transition at critical concentration pq from the behaviour of the conductance itself. We have also estimated the critical conductance, gc as gc = g(pq). By estimating the critical point for different values of electron Fermi energy E we have estimated the mobility-edge trajectory and it has been found to be consistent with the corresponding line in the p-E plane obtained by Soukoulis et al. (1987; 1992).