On thermal Nieh-Yan anomaly in topological Weyl materials

TL;DR

This paper explores a potential gravitational Nieh-Yan anomaly in topological Weyl materials, highlighting a universal, dimensionless parameter linked to geometry and topology, supported by spectral flow calculations at finite temperature.

Contribution

It proposes a temperature-dependent Nieh-Yan anomaly with a universal, dimensionless coefficient in topological Weyl materials, connecting geometry, topology, and chiral fields.

Findings

The anomaly involves a dimensionless parameter  b.

Supports the anomaly through spectral flow calculations at finite temperature.

Distinguishes the anomaly from non-universal UV scale dependent effects.

Abstract

We discuss the possibility of a gravitional Nieh-Yan anomaly of the type $\partial_\mu j^\mu_5 =\gamma T^2{\cal T}^a\wedge {\cal T}_a$ 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 $\Lambda$ 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.