On effects of electron-electron interactions in disordered electronic systems

Abstract

The effect of long-range electron-electron interactions on the existence of a mobility edge and on the characteristics of critical localization behaviour is studied for disordered systems by means of a 1/n-expansion in the finite temperature technique of many body theory. The lower critical dimension turns out to be two as in ensembles with interaction-free hamiltonians, and a subsequent d-2 expansion applies. In the case of time reversal invariance and in 0(1/n), cancellations of correlation contributions leave the conductivity behaviour unchanged when the Fermi energy approaches the still existing mobility edge(continuous transition). Many body effects however introduce criticality into one-particle properties and the density of states p(E_F) vanishes with the critical exponent β-1/(d-2)+0((d-2)°) when EF-Ec goes to zero on the metallic side f the transition. In the case of broken time reversal invariance the 0(1/n) approximation gives rise to speculations on a first order transition, but 0(1/n²) calculations are indispensable for a reliable conclusion.