Magic-angle twisted bilayer graphene (tBLG) displays a variety of symmetry-broken phases, correlated Chern insulators, orbital magnetism and superconductivity^{1,2,3,4,5,6,7,8}. In particular, the anomalous Hall effect has been observed when the bands are filled with an odd number of electrons per moiré unit cell^5,6,9, indicating the emergence of a zero-field orbital magnetic state with spontaneously broken time-reversal symmetry^10,11,12. Here we present measurements of two tBLG devices with twist angles slightly away from the magic angle and report the observation of the anomalous Hall effect at half filling of both the electron and hole moiré bands. We suggest that two factors—the increased band dispersion away from the magic angle, and substrate potentials from the encapsulating boron nitride—probably play critical roles in stabilizing a valley-polarized ground state at half filling. Our findings further expand the rich correlated phase diagram of tBLG, and indicate the need to develop a more complete understanding of its manifold of closely competing symmetry-breaking orders.

魔角扭曲双层石墨烯 (tBLG) 显示出各种对称破缺相、相关的陈绝缘体、轨道磁性和超导性^{1,2,3,4,5,6,7,8}。^{特别是，当每个莫尔晶胞5,6,9}的带子充满奇数电子时，观察到异常霍尔效应，这表明出现了具有自发破坏时间反转对称性的零场轨道磁态^{10 ,11,12}. 在这里，我们展示了两个 tBLG 器件的测量结果，它们的扭转角略微远离魔角，并报告了在电子和空穴莫尔带的半填充时对异常霍尔效应的观察。我们认为两个因素——远离魔角的增加的能带色散和来自封装氮化硼的衬底电位——可能在半填充时稳定谷极化基态中起关键作用。我们的研究结果进一步扩展了 tBLG 丰富的相关相图，并表明需要更全面地了解其密切竞争的对称破坏级的流形。