Hierarchy of Symmetry Breaking Correlated Phases in Twisted Bilayer Graphene

Twisted bilayer graphene (TBG) near the magic twist angle of $\sim1.1^{o}$ exhibits a rich phase diagram. However, the interplay between different phases and their dependence on twist angle is still elusive. Here, we explore the stability of various TBG phases and demonstrate that superconductivity near filling of two electrons per moir\'e unit cell alongside Fermi surface reconstructions, as well as entropy-driven high-temperature phase transitions and linear-in-T resistance occur over a range of twist angles which extends far beyond those exhibiting correlated insulating phases. In the vicinity of the magic angle, we also find a metallic phase that displays a hysteretic anomalous Hall effect and incipient Chern insulating behaviour. Such a metallic phase can be rationalized in terms of the interplay between interaction-driven deformations of TBG bands leading to Berry curvature redistribution and Fermi surface reconstruction. Our results provide an extensive perspective on the hierarchy of correlated phases in TBG as classified by their robustness against deviations from the magic angle or, equivalently, their electronic interaction requirements.