Abstract
Spontaneous orbital magnetism observed in twisted bilayer graphene (tBG) on nearly aligned hexagonal boron nitride (BN) substrate builds on top of the electronic structure resulting from combined G/G and G/BN double moire interfaces. Here we show that tBG/BN commensurate double moire patterns can be classified into two types, each favoring the narrowing of either the conduction or valence bands on average, and obtain the evolution of the bands as a function of the interlayer sliding vectors and electric fields. Finite valley Chern numbers $\pm 1$ are found in a wide range of parameter space when the moire bands are isolated through gaps, while the local density of states associated to the flat bands are weakly affected by the BN substrate invariably concentrating around the AA-stacked regions of tBG. We illustrate the impact of the BN substrate for a particularly pronounced electron-hole asymmetric band structure by calculating the optical conductivities of twisted bilayer graphene near the magic angle as a function of carrier density. The band structures corresponding to other $N$-multiple commensurate moire period ratios indicate it is possible to achieve narrow width $W \lesssim 30$ meV isolated folded band bundles for tBG angles $\theta \lesssim 1^{\circ}$.
Highlights
The electronic properties of magic angle twisted bilayer graphene and other graphene moiré systems have become an intense focus of research in recent years after observations of strong correlations and superconductivity in transport experiments [1,2,3,4,5,6]
We have investigated the electronic structure of commensurate double moiré patterns of twisted bilayer graphene (tBG) on boron nitride (BN) in an effort to understand the effects introduced by a BN substrate when it is brought to near alignment with the graphene layers and identify the conditions that are favorable for the appearance of gapped moiré bands with finite valley Chern numbers that lead to the anomalous Hall effects observed in experiments
The band structure of tBG has been calculated based on a continuum model that effectively accounts for vertical interlayer relaxations by using unequal interlayer tunneling parameters
Summary
The electronic properties of magic angle twisted bilayer graphene (tBG) and other graphene moiré systems have become an intense focus of research in recent years after observations of strong correlations and superconductivity in transport experiments [1,2,3,4,5,6]. In this paper we show that commensurate double moiré patterns of tBG on BN can have significant electron-hole asymmetric bands in addition to gaps between the moiré bands which provide the conditions for the formation of valley Chern bands prone to strong correlations. Our results provide a possible justification that the spontaneously broken-symmetry phases have been observed in experiments only for the conduction bands for the type 1 of double moiré arrangements [6,9], whereas correlated phases are likely for the valence bands for type 2 In both cases we find that isolation of the flatbands required to endow finite valley Chern numbers is facilitated by the opening of primary and secondary gaps.
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