Abstract— We show that interacting electrons in a flat Chern band can form, in addition to fractional Chern insulators, a chiral f-wave topological superconductor that hosts neutral Majorana fermion edge modes. Superconductivity emerges from an interaction-induced metallic state that exhibits anomalous Hall effect, as observed in rhombohedral graphene and near the ν=23 fractional Chern insulator in twisted transition metal dichalcogenides.
Introduction— The recent observation of fractional quantum anomalous Hall (FQAH) effect in moir´e materials [1–5] has reinforced interest in flat topological bands as a promising venue for realizing novel quantum matter. As a common feature, these materials host conjugate Chern bands with opposite Chern numbers in K and K′ valleys, which form time-reversed pairs [6, 7]. While narrow bandwidth generally enhances interaction effects, the nontrivial Bloch wavefunctions in topological bands drive interesting physics beyond the canonical Hubbard model. First, Coulomb interaction tends to drive spontaneous ferromagnetism and lift the degeneracy between conjugate Chern bands. Importantly, ferromagnetism occurs not only at integer band fillings [7–12], but extends over a wide and continuous range of partial band fillings [13–15]. This enables the FQAH effect to occur at fractional fillings when spin- and valley-polarized electrons populate a single Chern band and form a fractional Chern insulator (FCI) as theoretically predicted for twisted transition metal dicholcogenides [13, 16]. Notably, the FCI states observed so far exhibit the same quantized Hall plateaus as the celebrated Jain sequence of fractional quantum Hall states. This fact suggests some level of similarity between the underlying Chern band and the lowest Landau level. However, unlike Landau levels, a generic Chern band has non-uniform Berry curvature and quantum metric in the Brillouin zone, which can be experimentally tuned for example by the twist angle [7, 17–19]. It is therefore interesting to explore the possibility of novel phases in partially filled Chern bands that do not have a Landau level analog, when the band geometry is tuned away from the Landau level limit [20, 21]. In this work, we theoretically discover chiral superconductivity from purely repulsive electron interaction in flat Chern bands, even when electron’s kinetic energy is completely quenched in a dispersionless band. Our superconductor has f-wave pairing symmetry and is a time-reversal-breaking topological state hosting N = 3 branches of chiral Majorana fermion edge modes. Remarkably, we find that superconductivity and fractionalization can coexist in the same system, either at different filling factors, or at the same filling factor with thetransition between the two tuned by the geometry of the underlying Chern band.
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Liang Fu
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