Photogalvanic effects in symmetry broken nodal ring materials

Abstract

Nodal ring semimetals are a class of topological material characterized by a one-dimensional circular region of band crossing in momentum space. The presence of spin-orbit coupling, whether extrinsic or intrinsic, may change the parent nodal ring phase to a Weyl semimetal, Dirac semimetal, or topological insulator child phase. We investigate second harmonic generation and circular photogalvanic effect in the mid-infrared region of nodal ring materials where spin-orbit coupling produces a Weyl semimetal child phase (such as in $\mathrm{Zr}{\mathrm{Te}}_{5}$ and $\mathrm{Ca}{\mathrm{P}}_{3}$). Spin-orbit coupling breaks the symmetries protecting the nodal ring, inducing a nontrivial Berry curvature which gives rise to colossal photocurrents up to the order of ${10}^{3} \ensuremath{\mu}\mathrm{A}/{\text{V}}^{2}$ at the interband harmonic. Our results are found to be rather robust to parameters such as Fermi level, residual scattering rate, and the number of Weyl points. However, decreasing temperature tends to destroy the harmonic peaks and changing the nodal ring radius drastically alters the harmonic condition, shifting the peak frequency. Equivalent calculations and experiments have been carried out for intrinsic Weyl semimetals such as TaAs where the photocurrents calculated and observed were at least one order of magnitude smaller, highlighting that the parent nodal ring phase enhances these optical nonlinear phenomena.