Corrections to the self-consistent Born approximation for Weyl fermions

TL;DR

This paper investigates the accuracy of the self-consistent Born approximation for Weyl fermions, showing that a 1/N expansion justifies SCBA as N becomes large, while disorder strength expansion is invalid.

Contribution

It introduces a 1/N expansion framework to justify SCBA for Weyl fermions, clarifying its validity and limitations.

Findings

1/N expansion justifies SCBA for large N

Disorder strength expansion is not applicable

SCBA is the large N limit of Weyl fermions

Abstract

The average density of states of two- and three-dimensional Weyl fermions is studied in the self-consistent Born approximation (SCBA) and its corrections. The latter have been organized in terms of a 1/N expansion. It turns out that an expansion in terms of the disorder strength is not applicable, as previously mentioned by other authors. Nevertheless, the 1/N expansion provides a justification of the SCBA as the large N limit of Weyl fermions.