# Anomalous Hall viscosity at the Weyl semimetal/insulator transition

## TL;DR

This paper demonstrates that at the Weyl semimetal/insulator transition, 3D Lifshitz fermions develop an anomalous Hall viscosity at finite temperature, with a detailed theoretical framework and temperature dependence analysis.

## Contribution

It introduces a coupling of Lifshitz fermions to non-relativistic backgrounds using Newton-Cartan geometry and derives formulas for Hall viscosities across different Lifshitz scalings.

## Key findings

- Hall viscosity appears at the transition point.
- Viscosity expressions involve zeta functions.
- Temperature dependence follows the scaling exponent.

## Abstract

We show that 3D Lifshitz fermions arising as the critical theory at the Weyl semimetal/insulator transition naturally develop an anomalous Hall viscosity at finite temperature. We discuss how to couple the system to non-relativistic background sources for stress-tensor and momentum currents via a form of Newton-Cartan geometry with torsion and derive the Kubo formulas for the Hall viscosities. While the Lifshitz system that arises most naturally has scaling exponent $z=2$ we also generalize the theory for arbitrary Lifshitz scaling $z$ and show that, in the limit $z \to 0$, it may be given a Chern-Simons interpretation by dimensionally reducing along the anisotropic direction. The Hall viscosities are expressed in terms of zeta functions and their temperature dependence is dictated by the scaling exponent.