Torsional Responses and Liouville Anomaly in Weyl Semimetals with Dislocations

TL;DR

This paper develops a new theoretical framework to analyze torsional responses and anomalies in Weyl semimetals, revealing novel effects like a torsion-modified anomalous Hall effect and deepening understanding of topological responses.

Contribution

It introduces a quantum field theory-based approach combining Wigner transformation and band projection to derive semiclassical dynamics in Weyl semimetals with torsion.

Findings

Identification of a new pure torsion anomaly term.

Reproduction of the chiral vortical and torsional chiral magnetic effects.

Prediction of a torsion-modified anomalous Hall effect.

Abstract

Weyl nodes in three-dimensional Weyl semimetals break the Liouville equation, leading to the Liouville anomaly. Here we present a new approach to derive the semiclassical action and equations of motion for Weyl fermions in the presence of electromagnetic fields and torsions from the quantum field theory: combining the Wigner transformation with band projection operation. It has been shown that the Liouville anomaly, including a new pure torsion anomaly term, a mixing term between the electromagnetic fields and torsions as well as the conventional chiral anomaly, entirely differs from the counterpart of axial gauge fields. We find various torsional responses and reproduce the chiral vortical effect and the torsional chiral magnetic effect. A new torsion modified anomalous Hall effect due to the mixing term in the Liouville anomaly is predicted and its implementation is also discussed. Therefore, our work not only provides new insights into the torsional responses for Weyl fermions but also acts as a starting point to investigate their topological responses.