Unpaired Weyl Nodes from Long-Ranged Interactions: Fate of Quantum Anomalies

We study the effect of long-ranged interactions on Weyl semimetals. Such interactions can give rise to unpaired Weyl nodes, which we demonstrate by explicitly constructing a system with just a single node-a situation that is fundamentally forbidden by fermion doubling in noninteracting band structures. Adding a magnetic field, we investigate the fate of the chiral anomaly. Remarkably, as long as a system exhibits a single Weyl node in the absence of magnetic fields, arbitrarily weak fields qualitatively restore the lowest Landau level structure of a noninteracting Weyl semimetal. This underlines the universality of the chiral anomaly in the context of Weyl semimetals. We furthermore demonstrate how the topologically protected Fermi-arc surface states are modified by long-ranged interactions.