Linear and nonlinear optical and spin-optical response of gapped and proximitized graphene

The properties of graphene can be significantly modified by interaction with a commensurate substrate. Via proximity effects, both band gaps and substantial spin-orbit coupling can be induced, opening a route to novel applications. In this work, we ask whether the linear and nonlinear optical response can be applied to probe the underlying symmetry of gapped and proximitized graphene. Answering in the affirmative, we show that, in particular, optical second-harmonic generation is a highly sensitive tool for characterization. Importantly, the spin-orbit sublattice symmetry is clearly revealed by the optical spectra. In addition, the topological phase of the materials is revealed via linear and nonlinear spin-optical effects.