Nieh-Yan Anomaly: Torsional Landau Levels, central charge and anomalous thermal Hall effect

TL;DR

This paper investigates the Nieh-Yan anomaly through torsional Landau levels, revealing a connection to central charge and demonstrating its impact on thermal Hall conductance in Weyl semimetals.

Contribution

It introduces a novel perspective on the Nieh-Yan anomaly using torsional Landau levels and links the anomaly coefficient to the central charge and thermal Hall effect.

Findings

Torsional Landau levels are gapless but cancel anomaly contributions except the lowest level.

The anomaly coefficient equals the free energy density in (1+1) dimensions.

Thermal Hall conductance in Weyl semimetals is proportional to the central charge.

Abstract

The Nieh-Yan anomaly is the anomalous breakdown of the chiral U(1) symmetry caused by the interaction between torsion and fermions. We study this anomaly from the point of view of torsional Landau levels. It was found that the torsional Landau levels are gapless, while their contributions to the chiral anomaly are canceled, except those from the lowest torsional Landau levels. Hence, the dimension is effectively reduced from (3+1)-dimensional to (1+1)-dimensional. We further show that the coefficient of the Nieh-Yan anomaly is the free energy density in (1+1) dimensions. Especially, at finite temperature, the thermal Nieh-Yan anomaly is proportional to the central charge. The anomalous thermal Hall conductance in Weyl semimetals is then shown to be proportional to the central charge, which is the experimental fingerprint of the thermal Nieh-Yan anomaly.