Topological Scaling of Nonlinear Injection current and the Quantized Circular Photogalvanic Effect (CPGE)in tilted multi Weyl semimetals(mWSMs)
We develop a microscopic theory of nonlinear magneto-optical injection currents in multi-Weyl semimetals subjected to a uniform magnetic field. Using the Landau-level spectrum of a tilted multi-Weyl Hamiltonian with arbitrary monopole charge $ν$ as a starting point, we formulate a Kubo-type nonlinear response theory in the Landau-level basis and derive the second-order conductivity tensor. We identify distinct contributions originating from chiral-chiral, chiral-bulk, and bulk-bulk optical transitions, revealing characteristic monopole-charge scaling and sharp resonant structures governed by Landau-level selection rules and tilt-induced asymmetry. In the untilted limit, closed-form analytical expressions emerge that expose universal frequency thresholds and provide clear experimental signatures of higher-order Weyl topology. Our results establish nonlinear magneto-optical injection currents as a direct transport probe of chiral Landau levels and multi-Weyl topological charge.