  Van der Waals (vdW) heterostructures are an emergent class of metamaterials
comprised of vertically stacked two-dimensional (2D) building blocks, which
provide us with a vast tool set to engineer their properties on top of the
already rich tunability of 2D materials. One of the knobs, the twist angle
between different layers, plays a crucial role in the ultimate electronic
properties of a vdW heterostructure and does not have a direct analog in other
systems such as MBE-grown semiconductor heterostructures. For small twist
angles, the moir\'e pattern produced by the lattice misorientation creates a
long-range modulation. So far, the study of the effect of twist angles in vdW
heterostructures has been mostly concentrated in graphene/hexagonal boron
nitride (h-BN) twisted structures, which exhibit relatively weak interlayer
interaction due to the presence of a large bandgap in h-BN. Here we show that
when two graphene sheets are twisted by an angle close to the theoretically
predicted 'magic angle', the resulting flat band structure near charge
neutrality gives rise to a strongly-correlated electronic system. These flat
bands exhibit half-filling insulating phases at zero magnetic field, which we
show to be a Mott-like insulator arising from electrons localized in the
moir\'e superlattice. These unique properties of magic-angle twisted bilayer
graphene (TwBLG) open up a new playground for exotic many-body quantum phases
in a 2D platform made of pure carbon and without magnetic field. The easy
accessibility of the flat bands, the electrical tunability, and the bandwidth
tunability though twist angle may pave the way towards more exotic correlated
systems, such as unconventional superconductors or quantum spin liquids.
