Adler-Bell-Jackiw anomaly in Weyl semimetals: Application to pyrochlore iridates

Weyl semimetals are three-dimensional analogs of graphene where the energy of the excitations is a linear function of their momentum. Pyrochlore iridates $(A_2{\text{Ir}}_2{\text{O}}_7$ with A yttrium or a lanthanide element) are conjectured to be examples of such a system, with the low-energy physics described by 24 Weyl nodes. An intriguing possibility is that these materials provide a physical realization of the Adler-Bell-Jackiw anomaly. In this Rapid Communication we investigate the properties of pyrochlore iridates in an applied magnetic field. We find that the dispersion of the lowest Landau level depends on the direction of the applied magnetic field. Consequently, the velocity at low energies can be manipulated by changing the direction of the applied field. The resulting anisotropy in longitudinal conductivity is investigated.

Figure 1

The low-energy physics of pyrochlore iridates is described by linearly dispersing fermionic modes near nodes in the band structure. The position of Weyl nodes in the Brillouin zone is shown in the figure. There are three nodes, with the same chirality, located in the vicinity of the $L$ points, and nodes related by inversion have opposite chirality.

Figure 2

Top: The variation of the conductivity, for scattering potentials that only couple nodes that are related by inversion, as a function of the direction of magnetic field as a three-dimensional spherical plot. The radial distance of a point on the figure from the origin is a measure of the conductivity for the magnetic field along that direction. Bottom: A cut along the $Z-K$ direction.

Figure 3

Top: The variation of the conductivity, for scattering potentials that couple all nodes, as a function of the direction of magnetic field as a three-dimensional spherical plot. The radial distance of a point on the figure from the origin is a measure of the conductivity for the magnetic field along that direction. Bottom: A cut along the $Z-K$ direction.