Role of time reversal symmetry and tilting in circular photogalvanic responses

We study the role of time reversal symmetry (TRS) in the circular photogalvanic (CPG) responses considering a chiral Weyl semimetal (WSM), while a quantized CPG response is guaranteed by both the broken inversion symmetry and broken mirror symmetries. The TRS broken WSM yields one left and one right chiral Weyl node (WN), while there are two left and right chiral WNs for a TRS invariant WSM. We show that these features can potentially cause the quantization of a 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 depending on whether the system preserves or breaks the TRS. We find the CPG responses for a TRS invariant type-II WSM to be quantized at two and four times the topological charge of the activated WNs while the chemical potentials are, respectively, chosen in the vicinity of the energies associated with the left and right chiral WNs. By contrast, irrespective of the above choice of the chemical potential, the quantization in the CPG response is directly given by the topological charge of the activated WNs for the TRS broken case. Interestingly, we notice a nonquantized peak in the CPG response when the energies of the WNs associated with opposite chiralities are close to each other, as is the case for the TRS invariant type-I WSM considered here. Moreover, we show that the tilt can significantly modify the CPG response as the 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 the CPG response to relate with the final results and strengthen our analysis from the perspective of the lattice models.