Twisting two layers into a magic angle (MA) of ∼1.1 is found essential to create low energy flat bands and the resulting correlated insulating, superconducting, and magnetic phases in twisted bilayer graphene (TBG). While most of previous works focus on revealing these emergent states in MA-TBG, a study of the twist angle dependence, which helps to map an evolution of these phases, is yet less explored. Here, we report a magneto-transport study on one non-magic angle TBG device, whose twist angle θ changes from 1.25 at one end to 1.43 at the other. For θ = 1.25 we observe an emergence of topological insulating states at hole side with a sequence of Chern number | C | = 4 – | v |, where v is the number of electrons (holes) in moir unite cell. When θ > 1.25, the Chern insulator from flat band disappears and evolves into fractal Hofstadter butterfly quantum Hall insulator where magnetic flux in one moir unite cell matters. Our observations will stimulate further theoretical and experimental investigations on the relationship between electron interactions and non-trivial band topology.

发现将两层扭曲成约 1.1 的魔角 (MA) 对于在扭曲的双层石墨烯 (TBG) 中产生低能量平带和由此产生的相关绝缘、超导和磁性相至关重要。虽然以前的大多数工作都集中在揭示 MA-TBG 中的这些紧急状态，但对有助于绘制这些阶段演变图的扭转角依赖性的研究却很少被探索。在这里，我们报告了对一个非魔角 TBG 设备的磁传输研究，其扭转角θ从一端的 1.25 变为另一端的 1.43。对于θ = 1.25，我们观察到在孔侧出现拓扑绝缘状态，具有一系列陈数 | C | = 4 - | v |, 其中v是莫尔晶胞中的电子（空穴）数。当θ > 1.25 时，平带的 Chern 绝缘体消失，演变成分形​​ Hofstadter 蝴蝶量子霍尔绝缘体，其中一个莫尔晶胞中的磁通量很重要。我们的观察将激发对电子相互作用与非平凡能带拓扑之间关系的进一步理论和实验研究。