Surface Second Harmonic Generation from Topological Dirac Semimetal PdTe$_2$

Recent experiments and calculations in topological semimetals have observed anomalously strong second-order optical nonlinearity, but yet whether the enhancement also occurs at surfaces of topological semimetals in general remains an open question. In this work, we tackle this problem by measuring polarization-dependent and rotational-anisotropy optical second harmonic generation (SHG) from centrosymmetric type-II Dirac semimetal PdTe$_2$. We found the SHG to follow C$_{3v}$ surface symmetry with a time-varying intensity dictated by the oxidation kinetics of the material after its surface cleavage, indicating the surface origin of SHG. Quantitative characterization of the surface nonlinear susceptibility indicates a large out-of-plane response of PdTe$_2$ with $|\chi_{ccc}^{(2)}|$ up to 25 $\times$ 10$^{-18}$ m$^2$/V. Our results support the topological surfaces/interfaces as a new route toward applications of nonlinear optical effects with released symmetry constraints, and demonstrate SHG as a viable means to in situ study of kinetics of topological surfaces.