Chiral selection rules for multi-photon processes in two-dimensional honeycomb materials.

We examine the chirality-dependent optical selection rules in two-dimensional monolayer materials with honeycomb lattices, and, based on symmetry argument, we generalize these rules to multi-photon transitions of arbitrary orders. We also present the phase relations between incident and outgoing photons in such processes. The results agree nicely with our experimental observations of second- and third-harmonic generation. In particular, we demonstrate that the phase relation of chiral second-harmonic generation can serve as a handy tool for imaging domains and domain boundaries of these monolayers. Our results can benefit future studies on chirality-related optical phenomena and opto-electronic applications of such materials.