Hydrodynamics of topological Dirac semi-metals with chiral and $\mathbb{Z}_2$ anomalies

TL;DR

This paper develops a hydrodynamical model for topological Dirac semi-metals with both chiral and $ ext{Z}_2$ anomalies, revealing new kinetic coefficients influenced by vorticity and magnetic fields.

Contribution

It introduces a hydrodynamical framework incorporating the $ ext{Z}_2$ anomaly and two $U(1)$ gauge fields, highlighting novel modifications to the equations and kinetic coefficients.

Findings

Modified hydrodynamical equations due to $ ext{Z}_2$ anomaly

Emergence of new kinetic coefficients linked to vorticity and magnetic fields

Insights into the interplay of chiral and $ ext{Z}_2$ anomalies in topological materials

Abstract

We consider the hydrodynamical model of topological Dirac semi-metal possessing two Dirac nodes separated in momentum space along a rotation axis. It has been argued that the system in question, except the chiral anomaly, is endowed with the other one $\mathbb{Z}_2$. In order to model such a system we introduce two $U(1)$-gauge fields. The presence of the additional $\mathbb{Z}_2$ anomaly leads to the non-trivial modifications of hydrodynamical equations and to the appearance of new kinetic coefficients bounded with the vorticity and the magnetic parts of Maxwell and auxiliary $U(1)$-gauge fields.