Adler-Bell-Jackiw anomaly in Weyl semi-metals: Application to Pyrochlore Iridates

TL;DR

This paper explores the Adler-Bell-Jackiw anomaly in Weyl semimetals, specifically in pyrochlore iridates, demonstrating how magnetic field direction influences their magneto-conductivity, which could serve as an experimental signature.

Contribution

It provides a theoretical analysis of the anomaly in pyrochlore iridates, linking the anisotropic magneto-conductivity to the Weyl semimetal state.

Findings

Magneto-conductivity is highly anisotropic under magnetic fields.

The dispersion of the lowest Landau level depends on magnetic field direction.

Pyrochlore iridates exhibit properties consistent with Weyl semimetals.

Abstract

Weyl semimetals are three dimensional analogs of graphene where the energy of the excitations are a linear function of their momentum. Pyrochlore Iridates $(A_{2}Ir_{2}O_{7})$ with A =yttrium or lanthanide element) are conjectured to be examples of such a system, with the low energy physics described by twenty four Weyl nodes. An intriguing possibility is that these materials provide a physical realization of the Adler-Bell-Jackiw anomaly. In this letter 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. As a consequence the magneto-conductivity in an electric field, applied parallel to the magnetic field is highly anisotropic, providing a detectable signature of the semi-metallic state.