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In contrast to the fractional quantum Hall (FQH) effect, where electrondensity fixes the applied magnetic field, fractional Chern insulators (FCIs)can realize FQH states in comparatively weak or even zero magnetic fields.Previous theoretical work highlighted magic angle graphene as a promising FCIplatform, satisfying the twin requirements of flat bands andlowest-Landau-level-like quantum geometry. Indeed, recent experiments havedemonstrated FCIs in magic angle graphene with weak magnetic fields. Here weconduct a detailed theoretical study of the most prominent FCI state observed,and clarify the role of the magnetic field in stabilizing this state. Weintroduce two new technical tools: first, we generalize the notion of idealquantum geometry to Hofstadter minibands and, second, we extend theHartree-Fock theory of magic-angle graphene to finite field, to account for theinteraction generated bandwidth. We show that magnetic field both dramaticallyreduces the effective bandwidth and improves the quantum geometry for hostingFCIs. Using density matrix renormalization group (DMRG) simulations of amicroscopic model of magic angle graphene, we establish the regime of bandwidthand quantum geometry indicators where FCIs are stabilized. Furthercharacterizing the finite-field bands by the same quantities we show how azero-field charge density wave state gives way to an FCI state at a magneticflux consistent with experiment. We also speculate on the other FCIs seen inthe same experiments, including anomalous incompressible states andeven-denominator fractions which may host non-Abelian states. Finally, whenbandwidth is the limiting factor, we propose a range of experimental parameterswhere FCIs should appear at zero magnetic field.

Field-tuned and zero-field fractional Chern insulators in magic angle graphene