Strong disorder in nodal semimetals: Schwinger-Dyson--Ward approach

TL;DR

This paper introduces a non-perturbative method for accurately calculating disorder effects in semimetals, overcoming limitations of the self-consistent Born approximation, and validated against numerical data for various Hamiltonians.

Contribution

The authors develop a simple, non-perturbative approach using a differential equation on the imaginary axis to improve disorder self-energy calculations in semimetals.

Findings

Method yields quantitatively correct results for intermediate and strong disorder.

Approach performs well across various semimetal Hamiltonians.

Complementary to existing RG treatments of weak disorder.

Abstract

The self-consistent Born approximation quantitatively fails to capture disorder effects in semimetals. We present an alternative, simple-to-use non-perturbative approach to calculate the disorder induced self-energy. It requires a sufficient broadening of the quasiparticle pole and the solution of a differential equation on the imaginary frequency axis. We demonstrate the performance of our method for various paradigmatic semimetal Hamiltonians and compare our results to exact numerical reference data. For intermediate and strong disorder, our approach yields quantitatively correct momentum resolved results. It is thus complementary to existing RG treatments of weak disorder in semimetals.