Numerical studies of the Anderson transition in three-dimensional quantum site percolation

Abstract

Numerical studies of the dimensionless conductance g in 3D metal - insulator systems are reported. A site quantum percolation model is defined. It consists of two semi-infinite ideal metal electrodes and a disordered sample of size located between them. The disorder of the 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 is considered. Magnetic field is also introduced into the model. The conductance g is calculated using the Landauer - Büttiker formula and the Green's function technique. It is found that above the classical percolation threshold - that is, for - a second critical point exists denoted as . In the region , , where is the localization length, the system is localized, while in the range where the conductance tends to indicate metallic-type behaviour. By fitting the estimated data on versus ln g to the approximate relation for the scaling function valid in the vicinity of the critical point, the critical conductance is estimated to be and the correlation length critical exponent is estimated to be . Using a finite-size scaling technique and are also found. Both estimates of are expressed in units of and are in good agreement with one another. It is found that in the region where the system indicates positive magnetoconductance typical for a disorder-induced localized states phase, while in the region the magnetoconductance is negative as expected for an extended states phase.