Recent angle resolved photoemission spectroscopy measurements have identified an inversion symmetry breaking Weyl semimetal phase in TaAs and NbAs. In an inversion symmetry breaking Weyl semimetal the left and the right handed Weyl points can occur at different energies and the energy mismatch between the Weyl points of opposite chirality is known as the chiral chemical potential. In the presence of the chiral chemical potential, the nontrivial Berry curvature of the Weyl fermions gives rise to the emph{dynamic} chiral magnetic effect. This describes how a time dependent magnetic field leads to an electrical current along the applied field direction, which is also proportional to the field strength. We derive a general formula for the dynamic chiral magnetic conductivity of the inversion symmetry breaking Weyl semimetal. We show that the measurement of the natural optical activity or rotary power provides a direct confirmation of the existence of the dynamic chiral magnetic effect in inversion symmetry breaking Weyl semimetals.
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