A properly strained graphene monolayer or bilayer is expected to harbour periodic pseudo-magnetic fields with high symmetry, yet to date, a convincing demonstration of such pseudo-magnetic fields has been lacking, especially for bilayer graphene. Here, we report a definitive experimental proof for the existence of large-area, periodic pseudo-magnetic fields, as manifested by vortex lattices in commensurability with the moiré patterns of low-angle twisted bilayer graphene. The pseudo-magnetic fields are strong enough to confine the massive Dirac electrons into circularly localized pseudo-Landau levels, as observed by scanning tunneling microscopy/spectroscopy, and also corroborated by tight-binding calculations. We further demonstrate that the geometry, amplitude, and periodicity of the pseudo-magnetic fields can be fine-tuned by both the rotation angle and heterostrain. Collectively, the present study substantially enriches twisted bilayer graphene as a powerful enabling platform for exploration of new and exotic physical phenomena, including quantum valley Hall effects and quantum anomalous Hall effects.

中文翻译：

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低角度扭曲双层石墨烯中的大面积，周期性和可调谐本征伪磁场。

期望适当应变的石墨烯单层或双层具有高对称性的周期性伪磁场，但迄今为止，仍缺乏令人信服的此类伪磁场的证明，尤其是对于双层石墨烯。在这里，我们报告了存在大面积周期性伪磁场的确定性实验证据，如与低角度扭曲双层石墨烯的莫尔条纹相称的漩涡晶格所显示。伪磁场的强度足以将大量狄拉克电子限制在圆形局部的伪朗道能级，如通过扫描隧道显微镜/光谱学观察到的那样，并且还通过紧密结合计算得到证实。我们进一步证明了几何形状，振幅，伪磁场的周期性可以通过旋转角和异应变两者进行微调。总的来说，本研究极大地丰富了扭曲的双层石墨烯，为探索新的和奇特的物理现象（包括量子谷霍尔效应和量子异常霍尔效应）提供了强大的支持平台。