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

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.