Consequences of Chern bands in twisted bilayer graphene

In magic angle twisted bilayer graphene (TBG), alignment of hexagonal Boron Nitride (h-BN) substrate with one or both graphene monolayers can lead to nearly flat Chern bands labeled by valley and spin indices. At odd-fillings, we discuss how interaction effects in topologically non-trivial bands lead to a ferromagnetic Chern insulator with an anomalous Hall conductance that has been recently observed [1,2]. At the even filling of 2 of 4 conduction bands, we argue that charged skyrmions (allowed by Chern bands) offer a natural explanation of the magnetoresistance [1]. Finally, we discuss how the Chern character of the bands also places strong constraints on superconductivity in TBG.

[1] Sharpe, Fox et al; Science, 365, 605-608 (2019)
[2] Serlin, Tschirhart, Polshyn et al; arXiv:1907.00261