Origin of the mixed axial–gravitational anomaly in NbP

Determine whether the mixed axial–gravitational anomaly detected in the Weyl semimetal NbP arises from thermoelectrical transport in flat space-time or from a gravitational fourth-order derivative contribution that induces a fluid velocity, thereby identifying the primary physical mechanism responsible for the anomaly.

Background

The paper discusses chiral fermions in Weyl semimetals and notes that gravitational anomalies have observable consequences, including the mixed axial–gravitational anomaly detected in NbP. However, the physical mechanism generating this anomaly is not settled, with competing explanations involving conventional thermoelectric transport in flat space-time versus genuinely gravitational contributions modeled by higher-order derivative terms. Clarifying the origin is important for understanding how geometry and curvature manifest in transport phenomena of topological quantum materials.

References

Notably, the mixed axial-gravitational anomaly has already been detected in NbP [weyl3]. The anomaly's origin remains unsettled as to what is the main cause besides the breakdown of classical symmetry at the quantum level, either (i) it is tied to thermoelectrical transport in flat space-time [weyl21] or (ii) that the gravitational contribution (4${\rm th}$ order in derivatives) gives rise to a fluid velocity, a geometrical effect.

— Quantum matter and gravitation: photons in a waveguide  (2404.04277 - Atanasov et al., 2024) in Introduction