  The circular photogalvanic effect (CPGE) is the only possible quantized
signal in Chiral Weyl and multi-fold semimetals with inversion and mirror
symmetries broken. Here, we review CPGE in the chiral multifold semimetals in
terms of classification of CPGE tensor, the quantization of CPGE from k.p
effective model and topological semimetal RhSi family. Firstly, we give
complete symmetric analysis of CPGE tensors for all nonmagnetic point groups,
and get a table classifying matrix of response tensors. Secondly, the CPGE
becomes a quantized response in the noncentrosymmetric topological semimetals,
and depends on the Chern number of multifold fermions. Based on k.p effective
model with linear dispersion, detailed derivations about the quantization of
CPGE are given. Finally, according to ab-initio analysis for the quantized CPGE
based on noninteracting electronic structures, we review previous reports and
make new calculations for the chiral topological semimetals in RhSi family,
which can be separated into two groups. The first group, including RhSi, PtAl
and CoSi, can be the promising candidates to exhibit a quantized CPGE trace,
while the second group includes PdGa, PtGa and RhSn without a quantization.
