Axial anomaly and longitudinal magnetoresistance of a generic three dimensional metal

TL;DR

This paper demonstrates that the axial anomaly universally occurs in three-dimensional metals under parallel electric and magnetic fields, affecting longitudinal magnetoresistance depending on impurity scattering and band structure, with implications for various materials.

Contribution

It provides a comprehensive quantum mechanical analysis of axial anomaly effects on magnetoresistance in generic 3D metals, including impurity scattering influences and comparison with experimental observations.

Findings

Ionic impurities cause large positive magnetoconductivity proportional to B^2.

Neutral impurities can lead to both positive and negative magnetoresistance.

The magnetoresistance behavior varies with impurity type and band structure, showing initial negativity followed by positivity.

Abstract

We show that the emergence of the axial anomaly is a universal phenomenon for a generic three dimensional metal in the presence of parallel electric ($E$) and magnetic ($B$) fields. In contrast to the expectations of the classical theory of magnetotransport, this intrinsically quantum mechanical phenomenon gives rise to the longitudinal magnetoresistance for any three dimensional metal. However, the emergence of the axial anomaly does not guarantee the existence of negative longitudinal magnetoresistance. We show this through an explicit calculation of the longitudinal magnetoconductivity in the quantum limit using the Boltzmann equation, for both short-range neutral and long-range ionic impurity scattering processes. We demonstrate that the ionic scattering contributes a large positive magnetoconductivity $\propto B^2$ in the quantum limit, which can cause a strong negative magnetoresistance for any three dimensional or quasi-two dimensional metal. In contrast, the finite range neutral impurities and zero range point impurities can lead to both positive and negative longitudinal magnetoresistance depending on the underlying band structure. In the presence of both neutral and ionic impurities, the longitudinal magnetoresistance of a generic metal in the quantum limit initially becomes negative, and ultimately becomes positive after passing through a minimum. We discuss in detail the qualitative agreement between our theory and recent observations of negative longitudinal magnetoresistance in Weyl semimetals TaAs and TaP, Dirac semimetals Na$_3$Bi, Bi$_{1-x}$Sb$_x$, and ZrTe$_5$, and quasi-two dimensional metals PdCoO$_2$, $\alpha$-(BEDT-TTF)$_2$I$_3$ which do not possess any bulk three dimensional Dirac or Weyl quasiparticles.