Crystal symmetry plays a central role in governing a wide range of fundamental physical phenomena. One example is nonlinear optical second harmonic generation (SHG), which requires inversion symmetry breaking. We report a unique stacking-induced SHG in graphene trilayers, whose individual monolayer sheet is centrosymmetric. Depending on layer stacking sequence, we observe a strong optical SHG in a Bernal ABA-stacked non-centrosymmetric trilayer, while it vanishes in a 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 an otherwise homogeneous graphene trilayer. The extracted second-order nonlinear susceptibility of the ABA trilayer is surprisingly large, comparable to the best known two-dimensional 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.

中文翻译：

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堆叠对称性控制着石墨烯三层中的二次谐波的产生。

晶体对称性在控制广泛的基本物理现象中起着核心作用。一个示例是非线性光学二次谐波生成（SHG），它需要反转对称中断。我们报告了石墨烯三层中的一个独特的堆叠诱导SHG，其单个单层片是中心对称的。根据层堆叠顺序，我们在Bernal ABA堆叠的非中心对称三层中观察到了强烈的光学SHG，而在菱形ABC堆叠的三面体中消失了，这保留了反型对称性。由于不同的堆叠对称性，这种高度对比的SHG使我们能够绘制出在其他情况下均质的石墨烯三层中的ABA和ABC晶畴。提取的ABA三层二阶非线性磁化率出乎意料的大，可与通过激子共振增强的最著名的二维半导体相媲美。我们的结果揭示了一种新颖的堆叠顺序诱导的非线性光学效应，并释放了研究预测依赖堆叠的ABA和ABC石墨烯三层的有趣物理现象的机会。