Anomalous Hall Effect in Weyl Metals

We present a theory of the anomalous Hall effect (AHE) in a doped Weyl semimetal, or Weyl metal, including both intrinsic and extrinsic (impurity scattering) contributions. We demonstrate that a Weyl metal is distinguished from an ordinary ferromagnetic metal by the absence of the extrinsic and the Fermi surface part of the intrinsic contributions to the AHE, as long as the Fermi energy is sufficiently close to the Weyl nodes. The AHE in a Weyl metal is thus shown to be a purely intrinsic, universal property, fully determined by the location of the Weyl nodes in the first Brillouin zone.

Figure 1

(a) Plot of the band edges along the $z$ direction in momentum space for the two bands that touch at the Weyl nodes, using the specific expression for $\mathrm{\Delta }(k_z)$ from the multilayer model of Ref. [4]. (b) Field lines of the Berry curvature in the $k_y=0$ plane, for the same band structure as in (a). Corresponding Fermi surface section is shown by the two contours, enclosing the Weyl nodes.

Figure 2

Plot of the total anomalous Hall conductivity (solid line), ${\sigma }_{xy}^{\mathrm{I}}$ (dashed line) and ${\sigma }_{xy}^{\mathrm{II}}$ (dotted line) versus the Fermi energy for the same system as in Fig. 1. The plateaulike feature in ${\sigma }_{xy}$ correlates with the range of the Fermi energies, for which the Fermi surface consists of two separate sheets, each enclosing a single Weyl node. The energy units are the same as in Fig. 1.