Elastic Gauge Fields in Weyl Semimetals

TL;DR

This paper demonstrates that elastic deformations in Weyl semimetals act as pseudo gauge fields, leading to novel chiral electron-phonon couplings and measurable effects like phonon Hall viscosity, revealing new topological responses.

Contribution

It derives the form of elastic gauge fields in Weyl semimetals and shows their chiral coupling, providing a new example of axial gauge fields in three dimensions.

Findings

Elastic deformations couple as pseudo gauge fields in Weyl semimetals.

Chiral electron-phonon coupling leads to axial gauge fields.

Non-zero phonon Hall viscosity at zero temperature.

Abstract

We show that, as it happens in graphene, elastic deformations couple to the electronic degrees of freedom as pseudo gauge fields in Weyl semimetals. We derive the form of the elastic gauge fields in a tight-binding model hosting Weyl nodes and see that this vector electron-phonon coupling is chiral, providing an example of axial gauge fields in three dimensions. As an example of the new response functions that arise associated to these elastic gauge fields, we derive a non-zero phonon Hall viscosity for the neutral system at zero temperature. The axial nature of the fields provides a test of the chiral anomaly in high energy with three axial vector couplings.