Graphene is the name given to a flat monolayer of carbon atoms tightly packed into a two-dimensional (2D) honeycomb lattice, and is a basic building block for graphitic materials of all other dimensionalities. It can be wrapped up into 0D fullerenes, rolled into 1D nanotubes or stacked into 3D graphite. The carbon-carbon bond length in graphene is about 0.142 nm. Graphene sheets stack to form graphite with an interplanar spacing of 0.335 nm, which means that a stack of 3 million sheets would be only one millimeter thick. Graphene is the basic structural element of some carbon allotropes including graphite, charcoal, carbon nanotubes, and fullerenes. It can also be considered as an indefinitely large aromatic molecule, the limiting case of the family of flat polycyclic aromatic hydrocarbons.Theoretically, graphene (or ?2D graphite?) has been studied for sixty years, and is widely used for describing properties of various carbon-based materials.
The charge carriers in graphene have a unique nature. Its charge carriers mimic
relativisticparticles and are more easily and naturally described starting withthe Dirac equation rather than the Schr?dinger equation. Although there is nothing particularly relativistic about electronsmoving around carbon atoms, their interaction with the periodicpotential of graphene?s honeycomb lattice gives rise to newquasiparticles that at low energies E are accurately described bythe (2+1)-dimensional Dirac equation with an eff ective speed oflight vF ? 106 m/s. Th ese quasiparticles, called massless Diracfermions, can be seen as electrons that have lost their rest mass m0or as neutrinos that acquired the electron charge e. The relativisticlikedescription of electron waves on honeycomb lattices has beenknown theoretically for many years, never failing to attract attention,and the experimental discovery of graphene now provides a way toprobe quantum electrodynamics (QED) phenomena by measuringgraphene?s electronic properties.
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