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We propose and study generic multi-Weyl semimetal (mWSM) lattice Hamiltoniansthat break particle-hole symmetry. These models fall into two categories: modelI (model II) where the gap and tilt terms are coupled (decoupled) can hosttype-I and type-II Weyl nodes simultaneously (separately) in a hybrid phase(type-I and type-II phases, respectively). We concentrate on the question ofhow anisotropy and non-linearity in the dispersions, gaps and tilt termsinfluence diffusive second order transport quantities namely, the circularphotogalvanic effect (CPGE) and the Berry curvature dipole (BCD) as well asfirst order Magnus Hall effect (MHE) in the ballistic limit. The signatures oftopological charges are clearly imprinted in the quantized CPGE response forthe hybrid mWSM phase in model I. Such a quantization is also found in thetype-I WSM phase for model II, however, the frequency profiles of the CPGE inthese two cases is distinctively different owing to their different banddispersion irrespective of the identical topological properties. Thecontributions from the vicinity of Weyl nodes and away from the WNs are clearlymanifested in the BCD response, respectively, for model I model II. The Fermisurface properties for the activated momentum lead to a few hallmark featureson the MHE for both the models. Furthermore, we identify distinguishingsignatures of the above responses for type-I, type-II and hybrid phases toprovide an experimentally viable probe to differentiate these WSMs phases.

Distinct signatures of particle-hole symmetry breaking in transport coefficients for generic multi-Weyl semimetals