Disordered electron system with long-range correlated impurities

Abstract

The authors consider a d-dimensional electron gas in the presence of random potentials with Gaussian long-range correlations decaying with a power law mod x mod -d- sigma . They use the method of renormalised perturbation theory with dimensional regularisation and minimal subtraction to study the singular behaviour of a theory where the generating functional is the configurational average of the replicated vacuum amplitude. Calculations are carried out to one-loop order in a double expansion in in =4-d and sigma . They obtain a new long-range fixed point for sigma <0, 2 sigma < in < sigma that is unstable along one direction in parameter space and it is interpreted as describing the localisation transition at high dimensionality. From the solution of the RG equation they derive the scaling law for the conductivity.