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Graphene is a single layer of carbon chemical atoms arranged in a honeycomb lattice. A nearby gate can select predominantly Electron or electron hole conduction, as demonstrated by the graphene exfoliation and field-effect experiments.^[ref]

A useful question is how geometry changes motion. The nearest-neighbour model of graphene starts with three equivalent bonds from each site and two sites per primitive cell. Interference between those three hopping paths makes two energy bands meet; near their meeting, energy grows linearly with distance in wave vector. The resulting Dirac cones explain why an atomic sheet can imitate one aspect of a relativistic particle while remaining an ordinary material with contacts, defects and boundaries.

Andre Geim, Konstantin Novoselov and collaborators mechanically cleaved graphite, identified thin flakes, and fabricated multi-terminal Hall bars on oxidized silicon. A substrate gate changed the carrier density; longitudinal electrical resistance and the Hall coefficient supplied different checks. The 2004 report included one-, two- and three-layer devices and described a few-layer semimetal interpretation. Layer identification and electrical control were separate experimental achievements.^[ref]

The 2005 monolayer study used an optical microscope, electron microscopy and atomic force microscopy to select monolayers. It then measured Shubnikov-de Haas oscillations as temperature, gate voltage and magnetic field varied. Their damping inferred a density-dependent cyclotron effective mass; comparison with oscillation frequency tested a linear dispersion relation. A comparison with two-layer devices also distinguished their quantum Hall effect sequences. These are complementary tests of the monolayer model, rather than consequences of finding a thin-looking flake alone.^[ref]