Induced axion-phason field in Weyl semimetals

The Weyl semimetal in a constant magnetic field is investigated with the ground state for the lowest (n = 0) Landau levels corresponding to spin-down (sigma(3) = -1). In the presence of an electron-phonon coupling in the ground state, an attractive interaction for the polarized spin and opposite chirality is generated. A two-body attractive interaction projected to the two lowest (n = 0) chiral Landau levels with the same spin polarization is obtained. The higher Landau level states (n not equal 0) are treated at the one-loop approximation with the two chiralities containing spins polarized as sigma(3) = +/- 1. Using the chiral anomaly in one dimension we show that the sliding phase is controlled by the electric field. This theory, for a Weyl semimetal with two nodes in the direction of the applied magnetic field, gives rise to a sliding charge density wave observed by Gooth et al. [Nature (London) 575, 315 (2019].