Spectral Theorems for Generalized Weyl Nodes with Impurities in a Magnetic Field

TL;DR

This paper establishes spectral theorems for Weyl nodes with impurities, demonstrating that magnetic fields prevent localization and confirming the chiral magnetic effect across various topologies.

Contribution

It provides rigorous spectral results for Weyl nodes with impurities and proves the chiral magnetic effect for arbitrary topological configurations.

Findings

Density of states remains gapless under magnetic fields with impurities.

Magnetic fields prevent Anderson localization in Weyl semimetals.

Chiral magnetic effect is rigorously proven for all Weyl node topologies.

Abstract

We prove a few spectral theorems for the density of states of a Weyl node with arbitrary topology. We show that the density of extended states of a Weyl node with random impurity potentials remains gapless in the presence of a magnetic field. Therefore, a magnetic field precludes Anderson localization in Weyl semi-metals, when inter-node transitions are suppressed for smooth enough potentials. We also provide a rigorous quantum mechanical proof of the chiral magnetic effect for arbitrary topology of a Weyl node.