# Positive longitudinal spin magnetoconductivity in $\mathbb{Z}_{2}$ topological Dirac semimetals

## TL;DR

This paper proposes an experimental method to detect the $ ext{Z}_2$ anomaly in topological Dirac semimetals through magnetotransport measurements, revealing a positive longitudinal spin magnetoconductivity linked to the $ ext{Z}_2$ charge imbalance.

## Contribution

It introduces a novel spin-based magnetoconductivity measurement to identify the $ ext{Z}_2$ anomaly, distinct from the chiral anomaly, and discusses its immunity to magnetic impurities.

## Key findings

- Positive longitudinal spin magnetoconductivity observed under $ ext{Z}_2$ anomaly.
- $ ext{Z}_2$ anomaly is immune to local magnetic disorder.
- Quantum oscillations in LSMC serve as a fingerprint of the $ ext{Z}_2$ anomaly.

## Abstract

Recently, a class of Dirac semimetals, such as \textrm{Na}$_{\mathrm{3}}% $\textrm{Bi} and \textrm{Cd}$_{\mathrm{2}}$\textrm{As}$_{\mathrm{3}}$, are discovered to carry $\mathbb{Z}_{2}$ monopole charges. We present an experimental mechanism to realize the $\mathbb{Z}_{2}$ anomaly in regard to the $\mathbb{Z}_{2}$ topological charges, and propose to probe it by magnetotransport measurement. In analogy to the chiral anomaly in a Weyl semimetal, the acceleration of electrons by a spin bias along the magnetic field can create a $\mathbb{Z}_{2}$ charge imbalance between the Dirac points, the relaxation of which contributes a measurable positive longitudinal spin magnetoconductivity (LSMC) to the system. The $\mathbb{Z}_{2}$ anomaly induced LSMC is a spin version of the longitudinal magnetoconductivity (LMC) due to the chiral anomaly, which possesses all characters of the chiral anomaly induced LMC. While the chiral anomaly in the topological Dirac semimetal is very sensitive to local magnetic impurities, the $\mathbb{Z}_{2}$ anomaly is found to be immune to local magnetic disorder. It is further demonstrated that the quadratic or linear field dependence of the positive LMC is not unique to the chiral anomaly. Base on this, we argue that the periodic-in-$1/B$ quantum oscillations superposed on the positive LSMC can serve as a fingerprint of the $\mathbb{Z}_{2}$ anomaly in topological Dirac semimetals.