Fractionalizing the Hofstadter Butterfly: fractional Chern insulators in graphene superlattices

Fractional quantum Hall physics could potentially occur not just in the flat Landau levels of an electron gas, but more generally in any band characterized by a topological Chern number. As elucidated by Thouless and coworkers, such “Chern bands” arise naturally from the interplay of a magnetic field and a periodic potential. Recently, graphene heterostructures have emerged as a platform for realizing such Chern bands, by using a moire pattern between graphene and a substrate to engineer an artificial superlattice. Not only can the fractal structure of the Hofstadter butterfly be detected, the UCSB's Young Lab has now observed new gapped phases of matter which occur when the Chern bands of the butterfly are fractionally filled. I will discuss the theoretical interpretation of their results, which suggest graphene will prove a fruitful testbed for the physics of "fractional Chern insulators."​