Conductivity and mobility edges in disordered systems. II. Further calculations for the square and diamond lattices

Abstract

For pt.I see ibid., vol.8, p.4150 (1975). Further calculations for the Anderson model (1972) of a disordered lattice and square lattice are described. For the diamond lattice the critical value of disorder needed to destroy extended states is found to be W/V=8, which is considerably less than earlier calculations gave. There is however a wide range for which states seem to be intermediate between extended and exponentially localised states. Calculations of the conductance for much larger samples of a square lattice than were previously studied show that states identified as extended have a conductance that gets less as the sample gets larger, so that some doubt is cast on earlier conclusions about the minimum metallic conductance in two dimensions. Studies of the parameter A= integral mod Psi alpha mod 4/( mod integral Psi alpha mod 2)2 for the square and diamond lattices are reported. This seems to decrease smoothly to zero as the mobility edge is approached, but, since it approaches zero as (Ec-E)delta with delta apparently less than unity, interaction effects should lead to a vanishing density of states at the mobility edge and to the coexistence of itinerant electrons and unpaired localised electrons when the Fermi energy is just above the mobility edge.