Anomalous transport of Weyl fermions in Weyl semimetals

We present a field theoretical model of anomalous transport in Weyl semimetals. We calculate the chiral magnetic and chiral vortical effect in the electric, axial (valley), and energy current. Our findings coincide with the results of a recent analysis using kinetic theory in the bulk of the material. We point out that the kinetic currents have to be identified with the covariant currents in quantum field theory. These currents are anomalous and the CME appears as anomalous charge creation/annihilation at the edges of the Weyl semimetal. We discuss a possible simultaneous experimental test of the chiral magnetic and the chiral vortical effect sensitive to the temperature dependence induced by the gravitational contribution to the axial anomaly.