On Thermal Nieh-Yan Anomaly in Topological Weyl Materials

We discuss the possibility of gravitational Nieh-Yan anomaly of the type ∂μj~5μ=γT2Ta∧Ta in topological Weyl materials, where T is temperature and T^a is the effective or emergent torsion. As distinct from the non-universal parameter ⋀ 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.