NUMERICAL-STUDIES OF THE ANDERSON TRANSITION IN 3-DIMENSIONAL QUANTUMSITE PERCOLATION

Numerical studies of the dimensionless conductance g in 3D metal-insul ator systems are reported. A site quantum percolation model is defined . It consists of two semi-infinite ideal metal electrodes and a disord ered sample of size L x L x L located between them. The disorder of th e sample is controlled by the metal fraction p of conducting particles randomly occupying the sites of the cubic lattice with probability p. A tight-binding one-electron Hamiltonian with diagonal disorder and a probability density of site energies of the form P(epsilon(n)) p = de lta(epsilon(n)) + (1 - p)delta(epsilon(n) - infinity) is considered. M agnetic field is also introduced into the model. The conductance g is calculated using the Landauer-Buttiker formula and the Green's functio n technique. It is found that above the classical percolation threshol d-that is, for p > p(c) similar or equal to 0.312-a second critical po int exists denoted as p = p(q). In the region p(c) < p < p(q), g simil ar to exp(-L/xi(loc)), where xi(loc) is the localization length, the s ystem is localized, while in the range where p > p(q) the conductance tends to indicate g similar to L metallic-type behaviour. By fitting t he estimated data on beta(g) versus In g to the approximate relation f or the scaling function beta valid in the vicinity of the critical poi nt, the critical conductance is estimated to be g(c) = 1.32 +/- 0.19 a nd the correlation length critical exponent is estimated to be v = 1.6 +/- 0.2. Using a finite-size scaling technique p(q) = 0.44 +/- 0.01 a nd g(c) = 1.28 +/- 0.09 are also found. Both estimates of g(c) are exp ressed in units of e(2)/h and are in good agreement with one another. It is found that in the region where p < p(q) the system indicates pos itive magnetoconductance typical for a disorder-induced localized stat es phase, while in the p > p(q) region the magnetoconductance is negat ive as expected for an extended stares phase.