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Twisted bilayer systems of 2D materials have generated great recent interest due to their ability to create new, tunable electronic behavior. Twisted bilayers, for example, have been shown to exhibit novel Mott insulator-like states as well as unconventional superconductivity.1-6 The Crommie group is actively pursuing this area of research.
The most famous twisted bilayer system is obtained by stacking one layer of graphene on top of another and rotating the two layers by a small twist angle, θ. This causes a moiré pattern to arise between the lattices of the two graphene layers (Fig. 1a). One can estimate the resulting twisted bilayer electronic structure by considering the separate Brillouin zones of the two layers (Fig. 1b). If we zoom in on the K points of the two layers (marked K1 and K2 in (Fig. 1b) then we see that the Dirac cones of the two layers shift with respect to one another in k-space as they are rotated by θ, and they intersect at points above and below the Dirac point. This leads to hybridization and avoided crossings in the graphene bands (Fig. 1d), thus inducing the formation of new, flat bands and van Hove singularities (Fig. 1e).