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 |Cband| = 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 |Cband| = 1 band. At filling ν = 2/3 and ν = 1/3, a 3×3 charge-ordered quantum Hall crystal and a Halperin fractional Chern insulator with Hall conductance |σH| = 2e2/3h 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. Incorporating spin-valley degrees of freedom, the study identifies an optimal filling regime νtotal = 3 + ν for realizing the above states and shows that inter-flavor interactions renormalize the bandwidth and stabilize all gapped phases even in realistic sublattice corrugation parameter regimes.

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 |Cband| = 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 |Cband| = 1 band. At filling ν = 2/3 and ν = 1/3, a 3×3 charge-ordered quantum Hall crystal and a Halperin fractional Chern insulator with Hall conductance |σH| = 2e2/3h 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. Incorporating spin-valley degrees of freedom, the study identifies an optimal filling regime νtotal = 3 + ν for realizing the above states and shows that inter-flavor interactions renormalize the bandwidth and stabilize all gapped phases even in realistic sublattice corrugation parameter regimes.

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 |Cband| = 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 |Cband| = 1 band. At filling ν = 2/3 and ν = 1/3, a 3×3 charge-ordered quantum Hall crystal and a Halperin fractional Chern insulator with Hall conductance |σH| = 2e2/3h 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. Incorporating spin-valley degrees of freedom, the study identifies an optimal filling regime νtotal = 3 + ν for realizing the above states and shows that inter-flavor interactions renormalize the bandwidth and stabilize all gapped phases even in realistic sublattice corrugation parameter regimes.

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 |Cband| = 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 |Cband| = 1 band. At filling ν = 2/3 and ν = 1/3, a 3×3 charge-ordered quantum Hall crystal and a Halperin fractional Chern insulator with Hall conductance |σH| = 2e2/3h 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. Incorporating spin-valley degrees of freedom, the study identifies an optimal filling regime νtotal = 3 + ν for realizing the above states and shows that inter-flavor interactions renormalize the bandwidth and stabilize all gapped phases even in realistic sublattice corrugation parameter regimes.