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A family of ideal Chern flat bands with arbitrary Chern number in chiral twisted graphene multilayers
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In this article, a family of twisted bilayer graphene (CTBG) multilayers with a single twist on top of the stacked layers was considered, and it was shown that the Berry curvature distribution can be continuously tuned while maintaining perfect quantum geometry.Abstract:
We consider a family of twisted graphene multilayers consisting of $n$-untwisted {chirally stacked layers, e.g. AB, ABC, etc,} with a single twist on top of $m$-untwisted {chirally stacked} layers. Upon neglecting both trigonal warping terms for the untwisted layers and the same sublattice hopping between all layers, the resulting models generalize several remarkable features of the chiral model of twisted bilayer graphene (CTBG). {In particular, they exhibit a set of magic angles which are identical to those of CTBG at which a pair of bands (i) are perfectly flat, (ii) have Chern numbers in the sublattice basis given by $\pm (n,-m)$ or $\pm (n+m-1,-1)$ depending on the stacking chirality, and (iii) satisfy the trace condition, saturating an inequality between the quantum metric and the Berry curvature, and thus realizing ideal quantum geometry}. We provide explicit analytic expressions for the flat band wavefunctions at the magic angle in terms of the CTBG wavefunctions. We also show that the Berry curvature distribution in these models can be continuously tuned while maintaining perfect quantum geometry. Similar to the study of fractional Chern insulators in ideal $C = 1$ bands, these models pave the way for investigating exotic topological phases in higher Chern bands for which no Landau level analog is available.read more
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Correlated insulator behaviour at half-filling in magic-angle graphene superlattices
Yuan Cao,Valla Fatemi,Ahmet Demir,Shiang Fang,Spencer Tomarken,Jason Luo,Javier Sanchez-Yamagishi,Kenji Watanabe,Takashi Taniguchi,Efthimios Kaxiras,Raymond Ashoori,Pablo Jarillo-Herrero +11 more
TL;DR: It is shown experimentally that when this angle is close to the ‘magic’ angle the electronic band structure near zero Fermi energy becomes flat, owing to strong interlayer coupling, and these flat bands exhibit insulating states at half-filling, which are not expected in the absence of correlations between electrons.
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Moiré bands in twisted double-layer graphene
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The electronic properties of bilayer graphene.
Edward McCann,Mikito Koshino +1 more
TL;DR: The tight-binding model is used to describe optical and transport properties including the integer quantum Hall effect, and the also discusses orbital magnetism, phonons and the influence of strain on electronic properties.
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Flat bands in slightly twisted bilayer graphene: tight-binding calculations
TL;DR: In this article, the authors found flat bands near Fermi level in slightly twisted bilayer graphene as a signature of a transition from a parabolic dispersion to the characteristic linear dispersion of graphene.
Journal ArticleDOI
Continuum model of the twisted graphene bilayer
TL;DR: In this article, the Fourier components of the spatially modulated hopping amplitudes of the twisted graphene bilayer were calculated analytically for any type of commensurate structures in the low-twist-angle limit.