  We study the role of time reversal symmetry (TRS) in the circular
photogalvanic (CPG) responses considering chiral Weyl semimetal (WSM) while a
quantized CPG response is guaranteed by broken of both inversion symmetry (IS)
and mirror symmetries. The TRS broken WSM yields one left and one right chiral
Weyl nodes (WNs) while there are two left and right chiral WNs for TRS
invariant WSM. We show that these features can potentially cause the
quantization of CPG response at higher values compared to the topological
charge of the underlying WSM. This is further supported by the fact that Berry
curvature and velocity behave differently whether the system preserves or
breaks the TRS. We find the CPG responses for TRS invariant type-II WSM to be
quantized at two and four times the topological charge of the activated WNs
while the chemical potential are respectively chosen in the vicinity of
energies associated with left and right chiral WNs. By contrast, irrespective
of the above choice of the chemical potential, the quantization in CPG response
is directly given by the topological charge of the activated WNs for TRS broken
case. Interestingly, we notice non-quantized peak in CPG response when energies
of WNs associated with opposite chiralities are close to each other as it is
the case for TRS invariant type-I WSM considered here. Moreover, we show that
the tilt can significantly modify the CPG response as velocity in the tilt
direction changes which enters into the CPG tensor through the Fermi
distribution function. Given these exciting outcomes, the second order CPG
response emerges as a useful indicator to characterize the system under
consideration. Furthermore, we investigate the momentum resolved structure of
CPG response to relate with the final results and strengthen our analysis from
the perspective of the lattice models.
