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Recent experiments and calculations in topological semimetals have observedanomalously strong second-order optical nonlinearity, but yet whether theenhancement also occurs at surfaces of topological semimetals in generalremains an open question. In this work, we tackle this problem by measuringpolarization-dependent and rotational-anisotropy optical second harmonicgeneration (SHG) from centrosymmetric type-II Dirac semimetal PdTe$_2$. Wefound the SHG to follow C$_{3v}$ surface symmetry with a time-varying intensitydictated by the oxidation kinetics of the material after its surface cleavage,indicating the surface origin of SHG. Quantitative characterization of thesurface nonlinear susceptibility indicates a large out-of-plane response ofPdTe$_2$ with $|\chi_{ccc}^{(2)}|$ up to 25 $\times$ 10$^{-18}$ m$^2$/V. Ourresults support the topological surfaces/interfaces as a new route towardapplications of nonlinear optical effects with released symmetry constraints,and demonstrate SHG as a viable means to in situ study of kinetics oftopological surfaces.

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