Fractional Chern insulators (FCIs) are lattice analogues of fractional quantum Hall states that may provide a new avenue toward manipulating non-abelian excitations. Early theoretical studies have predicted their existence in systems with energetically flat Chern bands and highlighted the critical role of a particular quantum band geometry. Magic angle twisted bilayer graphene (MATBG) supports flat Chern bands at zero magnetic field, and therefore offers a promising route toward stabilizing zero-field FCIs. In this talk, I will describe our recent local compressibility measurements with a scanning single electron transistor that allow us to unambiguously identify the existence of FCIs in MATBG. I will also discuss the critical role of quantum band geometry in stabilizing FCIs.
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