Generation of a Nernst Current from the Conformal Anomaly in Dirac and Weyl Semimetals

We show that a conformal anomaly in Weyl and Dirac semimetals generates a bulk electric current perpendicular to a temperature gradient and the direction of a background magnetic field. The associated conductivity of this novel contribution to the Nernst effect is fixed by a beta function associated with the electric charge renormalization in the material. We discuss the experimental feasibility of the proposed phenomenon.