COULOMB GAP IN THE DENSITY-OF-STATES OF DISORDERED METALS IN 2 DIMENSIONS

We calculate the effect of Coulomb interactions on the average density of states nu(omega) of two-dimensional disordered electrons. It is sh own that for weal; disorder the most singular terms in the perturbativ e expansion of nu(omega) call be summed by means of a simple gauge tra nsformation, which also establishes a relation between the low-frequen cy behavior of nu(omega) and the average conductivity sigma(omega). Us ing this relation, we show that if lim(omega-->0) sigma(omega) < infin ity, then nu(omega) similar to C \omega \/e(4) for omega --> 0, where C is a dimensionless constant and e is the charge of the electron. Thi s implies that a normal metallic state of disordered electrons in two dimensions is not a Fermi liquid.