Graphene bilayer systems are known to exhibit a band gap when the layer
symmetry is broken, by applying a perpendicular electric field. The resulting
band structure resembles that of a conventional semiconductor with a parabolic
dispersion. Here, we introduce a novel bilayer graphene heterostructure, where
single-layer graphene is placed on top of another layer of graphene with a
regular lattice of antidots. We dub this class of graphene systems GOAL:
graphene on graphene antidot lattice. By varying the structure geometry, band
structure engineering can be performed to obtain linearly dispersing bands
(with a high concomitant mobility), which nevertheless can be made gapped with
the perpendicular field. We analyze the electronic structure and transport
properties of various types of GOALs, and draw general conclusions about their
properties to aid their design in experiments.Comment: 13 pages, 10 figures, submitte
