Axial anomaly and longitudinal magnetoresistance of a generic three-dimensional metal

Pallab Goswami, J. H. Pixley, S. Das Sarma

Research output: Contribution to journalArticlepeer-review

155 Scopus citations


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 ∝B2 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 Na3Bi, Bi1-xSbx, and ZrTe5, and quasi-two-dimensional metals PdCoO2 and α-(BEDT-TTF)2I3, which do not possess any bulk three-dimensional Dirac or Weyl quasiparticles.

Original languageEnglish (US)
Article number075205
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number7
StatePublished - Aug 17 2015

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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