Critical point for localization/delocalization transition in 3D metal-insulator systems

Abstract

Numerical studies of dimensionless conductance g in 3D metal-insulator systems have been reported. A discrete lattice site quantum site-percolation model has been defined. It consists of two semi-infinite ideal metal electrodes and a disordered sample of size L multiplied by L multiplied by L located between them. Disorder of the sample is controlled by metal fraction p of conducting particles randomly occupying the sites of cubic lattice with probability p. Tight- binding Hamiltonian with diagonal disorder and probability density of site energies of the form P((epsilon) n) equals p(delta) ((epsilon) n) plus (1-p)(delta) ((epsilon) n - (infinity) ) has been considered. Magnetic field has also been introduced to the model. Conductance g has been calculated using Landauer-Buttiker formula and Green's function technique. It has been found that above classical percolation threshold, that is for p greater than pc approximately equals 0.312, a second critical point exists denoted as p equals pq. In the region pc less than p less than pq, g approximately equals exp(-L/(xi) loc), where (xi) loc is localization length, the system is localized while in the range p greater than pq conductance tends to indicate g approximately equals L metallic type behavior. By fitting the estimated data of (beta) (g) vs 1ng to the approximate relation for the scaling function (beta) valid in the vicinity of the critical point, critical conductance gc equals 1.32 plus or minus 0.19 and correlation length critical exponent v equals 1.6 plus or minus 0.2 have been estimated. It has been found that in p less than pq region the system indicates negative magnetoresistance typical for disorder induced localized states phase, while p greater than pq range, magnetoresistance is positive as expected for extended states phase.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.