Interaction effects on the chiral Lifshitz parity anomaly

Determine whether the gapless chiral Lifshitz state remains accessible by tuning the valley mass to zero in an interacting system, and determine how electron–electron interactions modify its anomalous Hall response.

Background

The paper establishes the parity-anomalous Hall response for noninteracting chiral Lifshitz fermions realized in multilayer Haldane models. In this construction, tuning the valley mass to zero produces a gapless node with quadratic, cubic, or quartic dispersion and a corresponding winding-controlled Hall response.

The authors note that electron–electron interactions could shift the critical tuning condition or destabilize the node through interaction-driven ordered phases, including gapped or nematic phases. They therefore leave unresolved whether the gapless state can still be reached by tuning an interacting system and how interactions would alter its Hall conductivity; addressing these questions requires specifying a microscopic interaction model.