Theory of Correlated Chern Insulators in Twisted Bilayer Graphene

The Chern insulating states observed in twisted bilayer graphene at a finite magnetic field—and extrapolating to a band filling 𝑠 at zero field—remain poorly understood. Unraveling their nature is an important open problem. 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≠±4, as well as with fractional 𝑠, and elucidate their nature.