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

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

Negative Longitudinal Magnetoresistance from the Anomalous N=0 Landau Level in Topological Materials

“…(7) for x=0.14 and x=0.19. In the trivial case for x=0.14, the MR is positive (Fig.3(d)), in agreement with the predictions of Goswami et al for point defects [40] and with our data (Fig.2(a)). In the topological regime for x=0.19, the model yields a negative MR when…”

“…[41] [42] In IV-VI systems, the scattering rate from ionized impurities is thus expected to be at least two-orders of magnitude smaller than that of narrow-gap III-V or II-VI materials. [40] [43] It is also well known that in Pb1-xSnxSe, doping is essentially caused by atomic vacancies that can be treated as point-like defects. From ref.…”

“…The magnetic-field dependence of Ef is plotted in Fig.3(a,b) using: (4) The magnetoconductivity for a 3D electron gas in the quantum limit, in the presence of point-like impurities, has recently been treated by Goswami et al [40] Although ref. [40] has also treated the problem of scattering by long-range ionized impurities, we neglect their impact in Pb1-xSnxSe because of its very large dielectric constant (>280). [41] [42] In IV-VI systems, the scattering rate from ionized impurities is thus expected to be at least two-orders of magnitude smaller than that of narrow-gap III-V or II-VI materials.…”

Chiral magnetic plasmons in anomalous relativistic matter

“…(C2) in Appendix C, the coefficient A 1 in front of this term is proportional to a magnetic or pseudomagnetic field. Also, the last term in polarization vector (63) captures the anomalous Faraday effect of Weyl materials, i.e., the rotation of polarization in the absence of a background magnetic field [66]. In terms of the electric susceptibility tensor, we obtain…”

“…The situation is further complicated by the fact that, in general, the relaxation time may depend on the model parameters, types of impurities, and background fields, e.g., see Refs. [63,64]. Here, however, we assume that the sample is sufficiently clean and the collisionless limit is valid.…”