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(epsilon(n)) p delta(epsilon(n)) + (1 - p)delta(epsilon(n) - infinity) is studied using the Landauer-Buttiker formalism and Green's function method. The dimensionless conductance g according to Landauer-Buttiker formula is calculated for a finite system of size L x L x L. The arithmetic and geometric (e((In g))) 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 = p(q) such that g decreases (exponentially) with L, for p < p(q) and it increases (linearly) with L when p > p(q). Thus, we have demonstrated the Anderson metal-insulator transition at critical concentration p(q) from the behaviour of the conductance itself. We have also estimated the critical conductance, g(c) as g(c) drop g(p(q)). 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).