Photogalvanic response in multi-Weyl semimetals

We investigate the dependence of the photogalvanic response of a twofold degenerate multi-Weyl semimetal on its topological charge, tilt, and chemical potential. We derive analytical expressions for the shift and injection conductivities for tilted charge -n Weyl points using a low-energy two-band effective Hamiltonian. We compute the response for more realistic tight-binding models of a double-Weyl semimetal with broken time-reversal symmetry to find significant deviations from the effective low-energy continuum model predictions. We analyze several different limits of these models, describe the nature of these deviations, and provide estimates of their dependence on the frequency and other model parameters. Our analysis provides a simple explanation for the first-principle calculation based frequency dependence of the injection current in SrSi2. We also obtain analytical results for the charge-4 Weyl semimetal using a new approach, providing all relevant information about the nature of its second-order dc response and the precise condition for observing quantized circular photogalvanic effect. This approach can easily be extended to a systematic study of second harmonic generation and first-order optical conductivity in charge-4 Weyl semimetals.