Moiré Commensurability and the Quantum Anomalous Hall Effect in Twisted Bilayer Graphene on Hexagonal Boron Nitride

Abstract

The quantum anomalous Hall (QAH) effect is sometimes observed in twisted bilayer graphene (tBG) when it is nearly aligned with an encapsulating hexagonal boron nitride (hBN) layer. We propose that the appearance or absence of the QAH effect in individual devices could be related to commensurability between the graphene/graphene and graphene/hBN moiré patterns. We identify a series of points in the $({\theta }_{\mathrm{GG}},{\theta }_{\mathrm{GBN}})$ twist-angle space at which the two moiré patterns are commensurate, allowing moiré band theory to be applied, and show that the band Chern numbers are in this case sensitive to a rigid in-plane hBN displacement. Given this property, we argue that the QAH effect is likely only when i) the $({\theta }_{\mathrm{GG}},{\theta }_{\mathrm{GBN}})$ twist-angle-pair is close enough to a commensurate point that the two moiré patterns yield a supermoiré pattern with a sufficiently long length scale, and ii) the supermoiré has a percolating topologically non-trivial QAH phase. For twist angles far from commensurability, the hBN layer acts as a source of disorder that can destroy the QAH effect. Our proposal can explain a number of current experimental observations. Further experimental studies that can test this proposal more directly are suggested.

References in corpus (10)

• The electronic properties of graphene
• Quantum Hall Ferromagnetism in Graphene
• Origin of band gaps in graphene on hexagonal boron nitride
• Electronic properties of graphene hexagonal boron nitride moiré superlattice
• New generation of moiré superlattices in doubly aligned hBN/graphene/hBN heterostructures
• Composite super-moiré lattices in double aligned graphene heterostructures
• Moiré band model and band gaps of graphene on hexagonal boron nitride
• Double moiré with a twist: super-moiré in encapsulated graphene
• Probing of valley polarization in graphene via optical second-harmonic generation
• Symmetry breaking in the double moiré superlattices of relaxed twisted bilayer graphene on hexagonal boron nitride

Cited by in corpus (3)

• Band Structure and Superconductivity in Twisted Trilayer Graphene
• Flat bands, strains, and charge distribution in twisted-bilayer hBN
• Electron-hole asymmetry and band gaps of commensurate double moire patterns in twisted bilayer graphene on hexagonal boron nitride