Abstract
A recent experiment reported a large anomalous Hall effect in Magic Angle Twisted Bilayer Graphene (TBG) aligned with a hexagonal boron nitride(h-BN) substrate at $\frac{3}{4}$ filling of the conduction band. In this paper we study this system theoretically, and propose explanations of this observation. We emphasize that the physics for this new system is qualitatively different from the pure TBG system. The aligned h-BN breaks in-plane two-fold rotation symmetry and gaps out the Dirac crossings of ordinary TBG. The resulting valence and conduction bands of each valley carry equal and opposite Chern numbers $C=\pm 1$. A useful framework is provided by a lattice extended Hubbard model for this system which we derive. An obvious possible explanation of the anomalous Hall effect is that at $3/4$-filling the system is a spin-valley polarized ferromagnetic insulator where the electrons completely fill a Chern band. We also examine an alternate more radical proposal of a compressible valley polarized but spin unpolarized composite ferm liquid metallic state. We argue that either state is compatible with current experiments, and propose ways to distinguish between them in the future. We also briefly discuss the physics at $1/2$ filling.
Highlights
Moiré superlattices from twisted van der Waals heterostructures have emerged as promising platforms to study strongly correlated effects with high tunability [1,2,3,4,5]
Correlated insulators and superconductors have been found in twisted bilayer graphene and ABC stacked trilayer graphene/hexagonal boron nitride (TG/h-BN) [2,3,4,5]
The twisted bilayer graphene (TBG)/h-BN system is in a different limit U ∼ W >, and the detailed many-body physics may differ from that discussed in Ref. [8]
Summary
Moiré superlattices from twisted van der Waals heterostructures have emerged as promising platforms to study strongly correlated effects with high tunability [1,2,3,4,5]. Very recently a large anomalous Hall effect was observed [6] in magic angle–twisted bilayer graphene (MA TBG) at conduction-band filling ν. [8], at total fillings νT = 1, 3 nearly flat ± Chern bands are an excellent platform for the quantum anomalous Hall effect, as well as other even more novel many-body states. [9] described a spin-valley polarized quantum anomalous Hall state in unaligned twisted bilayer graphene where C2T is broken by interaction effects. Combining the two valleys and projecting the Coulomb interaction yields an effective lattice “extended” Hubbard model suitable for TBG-hBN. This lattice model provides a useful framework to discuss the physics and may be useful for future numerical studies
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