Fractional Chern Insulators and Hofstadter Band Geometry in Magic-Angle Graphene*

Fractional Chern Insulators (FCIs) generalize the celebrated fractional quantum hall effect to the lattice setting. A number of theoretical proposals have suggested (hBN-aligned) magic-angle graphene (MATBG) is a prime candidate for realizing FCIs, as its bandstructure and quantum geometry are relatively close to that of the lowest Landau level. Indeed, this was borne out in a recent experiment, which observed 8 FCIs in hBN-MATBG at magnetic fields as low as 5 Tesla. This talk will examine a constellation of questions surrounding this experiment. Can we understand the appearance of these FCIs? What quantum geometric conditions are necessary to favor FCIs in the minibands of the Hofstadter butterfly? Can MATBG support FCIs without an external field?