The 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 finite CPG response is guaranteed by already broken 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 that the quantization in CPG response is twice and four times the topological charge of the activated WNs for TRS invariant WSM while the quantization is directly given by the topological charge for the activated WNs in TRS broken case. This clearly suggests that the anti-symmetric behavior of CPG response between two opposite WNs is lost for TRS invariant system referring to the unique transport signature of the above systems. Moreover, we find 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. Following the low-energy theory, we analytically understand the numerical results as obtained from the lattice models. 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.