We Introduce two New Technical Tools: First

Abstract:In contrast to the fractional quantum Hall (FQH) effect, where electron density fixes the utilized magnetic discipline, 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 FCI platform, satisfying the twin necessities of flat bands and lowest-Landau-level-like quantum geometry. Indeed, recent experiments have demonstrated FCIs in magic angle graphene with weak magnetic fields. Here we conduct an in depth theoretical research of essentially the most outstanding FCI state observed, and make clear the role of the magnetic subject in stabilizing this state. We introduce two new technical instruments: first, we generalize the notion of ideally suited quantum geometry to Hofstadter minibands and, second, we lengthen the Hartree-Fock theory of magic-angle graphene to finite discipline, to account for the interaction generated bandwidth. We present that magnetic area both dramatically reduces the efficient bandwidth and improves the quantum geometry for internet hosting FCIs. Using density matrix renormalization group (DMRG) simulations of a microscopic model of magic angle graphene, patrick's magic field we set up the regime of bandwidth and quantum geometry indicators the place FCIs are stabilized. Further characterizing the finite-discipline bands by the same quantities we present how a zero-area cost density wave state offers option to an FCI state at a magnetic flux in step with experiment. We also speculate on the opposite FCIs seen in the same experiments, including anomalous incompressible states and even-denominator fractions which can host non-Abelian states. Finally, when bandwidth is the limiting issue, we suggest a variety of experimental parameters the place FCIs ought to seem at zero magnetic area.


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