Akshay Kumar, Rahul Nandkishore
We demonstrate that flat bands with local Berry curvature arise naturally in chiral (ABC) multilayer graphene placed on a boron nitride (BN) substrate. The degree of flatness can be tuned by varying the number of graphene layers N. For N > 5 the bands become nearly flat, with a small bandwidth 5meV . The two nearly flat bands coming from the K and K' valleys cross along lines in the reduced zone. Weak intervalley tunneling turns the bandcrossing into an avoided crossing, producing two nearly flat bands with global Chern number zero, but with local Berry curvature. The flatness of the bands suggests that many body effects will dominate the physics, while the Berry curvature of the bands endows the system with a nontrivial quantum geometry. Multilayer graphene on BN thus provides a platform for investigating the interplay of interactions and quantum geometry which has no analog in the fractional quantum Hall effect. Flat bands with non-zero Chern number may also be realized by making use of magnetic adatoms, and explicitly breaking time reversal symmetry.
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http://arxiv.org/abs/1302.0855
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