Quantum anomalous Hall effects and emergent $\mathrm{SU}(2)$ Hall ferromagnets at fractional filling of helical trilayer graphene

Abstract

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 $|C_{band}|=2$ 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 $|C_{band}|=1$ band. At filling $\hat{I}½=2/3$ and $\hat{I}½=1/3$, a $\sqrt{3}\times \sqrt{3}$ charge-ordered quantum Hall crystal and a Halperin fractional Chern insulator with Hall conductance $|\ddot{I}{ƒ}_H|=2e^2/3h$ are predicted respectively, indicating strong particle-hole asymmetry of the system. At half-filling $\hat{I}½=1/2$, an extensively degenerate pseudospin Hall ferromagnet featuring emergent $\mathrm{SU}(2)$ 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 $\mathrm{SU}(2)$ quantum numbers even far away from the chiral limit. Incorporating spin-valley degrees of freedom, we identify an optimal filling regime $\hat{I}{½}_{\mathrm{total}}=3+\hat{I}½$ for realizing the above states. Notably, inter-flavor interactions renormalize the bandwidth and stabilize all the gapped phases even in realistic sublattice corrugation parameter regimes.