On thermal Nieh-Yan anomaly in topological Weyl materials

Abstract

We discuss the possibility of a gravitional Nieh-Yan anomaly of the type ${\partial }_{\mu }{j}_5^{\mu }=\gamma T^2{\mathcal{T}}^a\wedge {\mathcal{T}}_a$ in topological Weyl materials, where $T$ is temperature and ${\mathcal{T}}^a$ is the effective or emergent torsion. As distinct from the non-universal parameter $\Lambda$ in the conventional (zero temperature) Nieh-Yan anomaly -- with canonical dimensions of momentum -- the parameter $\gamma$ 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.

arXiv comment4 pages, submitted to JETP Lett. arXiv admin note: substantial text overlap with arXiv:1909.08936

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• Torsional Landau levels and geometric anomalies in condensed matter Weyl systems
• On thermal Nieh-Yan anomaly in Weyl superfluids
• Topological magnetotorsional effect in Weyl semimetals
• Chiral torsional effect with finite temperature, density and curvature
• Topological polarization, dual invariants, and surface flat band in crystalline insulators
• Hamiltonian approach to the torsional anomalies and its dimensional ladder
• Gravitomagnetic Helicity
• ${}^3$He Universe 2020
• Torsion at different scales: from materials to the Universe
• Torsion-induced chiral magnetic current in equilibrium
• Anomalous chiral transport with vorticity and torsion: Cancellation of two mixed gravitational anomaly currents in rotating chiral $p+ip$ Weyl condensates
• Parity violation in Poincaré gauge gravity
• Phonon helicity and Nieh-Yan Anomaly in the Kramers-Weyl semimetals of Chiral Crystals