Quantum Anomalous Hall Effects and Emergent SU(2) Hall Ferromagnets at Fractional Filling of Helical Trilayer Graphene

Helical trilayer graphene realizes a versatile moiré system for exploring correlated topological states emerging from high Chern bands. Motivated by recent experimental observations of anomalous Hall effects at fractional fillings of magic-angle helical trilayers, we focus on the higher Chern number |C₁₀₍₃|=2 band and explore gapped many-body Hall states beyond the conventional Landau level paradigm. Through extensive exact diagonalization, we predict novel phases unattainable in a single |C₁₀₍₃|=1 band. At filling ν=2/3 and ν=1/3, a sqrt3×sqrt3 charge-ordered quantum Hall crystal and a Halperin fractional Chern insulator with Hall conductance |σ₇|=2e^2/3h are predicted, respectively, indicating strong particle-hole asymmetry of the system. At half-filling ν=1/2, an extensively degenerate pseudospin Hall ferromagnet featuring emergent SU (2) symmetry is found without the band being flat. Inspired by striking robustness of the ferromagnetic degeneracy, we develop a method to unveil and quantify the emergent symmetry via pseudospin operator construction in the presence of band dispersion and Coulomb interaction and demonstrate persistence of the SU (2) quantum numbers even far away from the chiral limit. Incorporating spin-valley degrees of freedom, we identify an optimal filling regime νₓ₎ₓ₀₋=3+ν for realizing the above states. Notably, interflavor interactions renormalize the bandwidth and stabilize all the gapped phases even in realistic sublattice corrugation parameter regimes.