Stacking-symmetry governed second harmonic generation in graphene trilayers

Crystal symmetry plays a central role in governing a wide range of fundamental physical phenomena. One example is the nonlinear optical second harmonic generation (SHG), which requires inversion symmetry breaking. Here we report a unique stacking-induced SHG in trilayer graphene, whose individual monolayer sheet is centrosymmetric. Depending on layer stacking sequence, we observe a strong optical SHG in Bernal (ABA) stacked non-centrosymmetric trilayer, while it vanishes in rhombohedral (ABC) stacked one which preserves inversion symmetry. This highly contrasting SHG due to the distinct stacking symmetry enables us to map out the ABA and ABC crystal domains in otherwise homogeneous graphene trilayer. The extracted second order nonlinear susceptibility of the ABA trilayer is surprisingly large, comparable to the best known 2D semiconductors enhanced by excitonic resonance. Our results reveal a novel stacking order induced nonlinear optical effect, as well as unleash the opportunity for studying intriguing physical phenomena predicted for stacking-dependent ABA and ABC graphene trilayers.