On thermal Nieh-Yan anomaly in topological Weyl materials

We discuss the possibility of a gravitional Nieh-Yan anomaly of the type $\partial_μj^μ_5 =γT^2{\cal T}^a\wedge {\cal T}_a$ in topological Weyl materials, where $T$ is temperature and ${\cal T}^a$ is the effective or emergent torsion. As distinct from the non-universal parameter $Λ$ in the conventional (zero temperature) Nieh-Yan anomaly -- with canonical dimensions of momentum -- the parameter $γ$ is dimensionless. This suggests that the dimensionless parameter is fundamental, being determined by the geometry, topology and number of the number of chiral quantum fields without any explicit non-universal UV scales. This conforms with previous results in the literature, as well as spectral flow calculations using torsional magnetic field at finite temperature.

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