Role of time reversal symmetry and tilting in circular photogalvanic responses

Abstract

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.