# Quantitative analytical theory for disordered nodal points [Article and Erratum]

## TL;DR

This paper develops an analytical approach using the functional renormalization group to accurately evaluate the average density of states near disordered nodal points in materials like graphene and Weyl semimetals, matching numerical data.

## Contribution

It introduces a novel analytical method for disordered nodal points that surpasses previous approaches in accuracy for both 2D and 3D systems.

## Key findings

- Excellent agreement with numerical simulations in 2D
- Significant improvement over existing methods in 3D
- Provides a quantitative analytical framework for disorder effects

## Abstract

Disorder effects are especially pronounced around nodal points in linearly dispersing bandstructures as present in graphene or Weyl semimetals. Despite the enormous experimental and numerical progress, even a simple quantity like the average density of states cannot be assessed quantitatively by analytical means. We demonstrate how this important problem can be solved employing the functional renormalization group method and, for the two dimensional case, demonstrate excellent agreement with reference data from numerical simulations based on tight-binding models. In three dimensions our analytic results also improve drastically on existing approaches.