Theory of Correlated Chern Insulators in Twisted Bilayer Graphene

Magic -angle twisted bilayer graphene is the best -studied physical platform featuring moire<acute accent> potentialinduced narrow bands with nontrivial topology and strong electronic correlations. Despite their significance, the Chern insulating states observed at a finite magnetic field-and extrapolating to a band filling s at zero field-remain poorly understood. Unraveling their nature is among the most important open problems in the province of moire<acute accent>materials. Here, we present the first comprehensive study of interacting electrons in finite magnetic field while varying the electron density, twist angle, and heterostrain. Within a panoply of correlated Chern phases emerging at a range of twist angles, we uncover a unified description for the ubiquitous sequence of states with the Chern number t for (s, t) = +/-(0, 4), +/-(1, 3), +/-(2, 2), and +/-(3, 1). We also find correlated Chern insulators at unconventional sequences with s + t not equal +/- 4, as well as with fractional s, and elucidate their nature.