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

TL;DR

This paper predicts novel correlated topological phases in helical trilayer graphene at fractional fillings, including charge-ordered quantum Hall states and an emergent SU(2) symmetric pseudospin ferromagnet, using extensive exact diagonalization.

Contribution

It introduces the prediction of new fractional Chern insulator states and an emergent SU(2) Hall ferromagnet in helical trilayer graphene, beyond conventional models.

Findings

Prediction of a $rac{1}{3}$ fractional Chern insulator with Hall conductance $2e^2/3h$.

Identification of a $rac{2}{3}$ charge-ordered quantum Hall crystal.

Discovery of an SU(2) symmetric pseudospin Hall ferromagnet at half-filling.

Abstract

Helical trilayer graphene realizes a versatile moir\'e 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 $\nu=2/3$ and $\nu=1/3$, a $\sqrt{3}\times \sqrt{3}$ charge-ordered quantum Hall crystal and a Halperin fractional Chern insulator with Hall conductance $|\sigma_{H}|=2e^2/3h$ are predicted respectively, indicating strong particle-hole asymmetry of the system. At half-filling $\nu=1/2$, an extensively degenerate pseudospin Hall ferromagnet featuring emergent $\rm{SU}(2)$ 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 $\rm{SU}(2)$ quantum numbers even far away from the chiral limit. Incorporating spin-valley degrees of freedom, we identify an optimal filling regime $\nu_{\rm{total}}=3+\nu$ 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.