Localisation and conductivity studies on two-dimensional spatially disordered systems

The technique of numerical simulation on finite systems is used to study electron localisation and conductivity in two-dimensional systems for which the atoms are completely randomly distributed in space. The localisation criterion of Licciardello and Thouless (1975) is used to locate mobility edges and a calculation of the conductivity yields a value for the minimum metallic conductivity of 0.1 e 2 /h(cross). It is indicated through the use of simple perturbation theory that states near the band edges are localised on clusters of atoms at locally high density, as proposed by Kikuchi. Finally, the results for the density of states and conductivity are compared with those obtained by the analytic treatment of Matsubara and Toyozawa (1961) which has been adapted to two dimensions.