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.