Optical Response from Charge-Density Waves in Weyl Semimetals

Electron-phonon coupling has been predicted to influence magnetoelectric coupling in Weyl semimetals (WSM) through charge-density wave distortions. We investigate this current by calculating the collective mode contribution to response functions in quasi-1D lattice and continuous models of a time-reversal-breaking WSM coupled to charge-density wave order. We compare the collective mode contributions from the longitudinal conductivity in a WSM to the established 1D results at linear and nonlinear order. We pay particular attention to the role of symmetry in mediating the effects of both the sliding and amplitude collective modes. We find that with inversion symmetry there are non-vanishing currents generated by third order processes, including a material analog of a Higgs mechanism. We also show that tilting the linearly dispersing nodes of the WSM will enhance the sliding mode contribution to the longitudinal conductivity at zero frequency.