Coulomb Gap in the Density of States of Disordered Metals in Two Dimensions

TL;DR

This paper investigates how Coulomb interactions affect the density of states in two-dimensional disordered metals, revealing that such systems deviate from Fermi liquid behavior and exhibit a Coulomb gap at low frequencies.

Contribution

It demonstrates that Coulomb interactions induce a Coulomb gap in the density of states of 2D disordered metals and relates this to the low-frequency conductivity behavior.

Findings

Density of states approaches C|omega|/e^4 as omega approaches 0.

Normal 2D disordered metals are not Fermi liquids due to Coulomb interactions.

A gauge transformation sums the most singular perturbative terms.

Abstract

We calculate the effect of Coulomb interactions on the average density of states nu (omega) of two-dimensional disordered electrons. It is shown that for weak disorder the most singular terms in the perturbative expansion of nu (omega) can be summed by means of a simple gauge transformation, which also establishes a relation between the low-frequency behavior of nu (omega) and the average conductivity sigma (omega). Using this relation, we show that if lim_{omega rightarrow 0} sigma (omega) is finite, then nu (omega) approaches C | omega | / e^4 for omega rightarrow 0, where C is a dimensionless constant and e is the charge of the electron. This implies that a normal metallic state of disordered electrons in two dimensions is not a Fermi liquid.