The Role of Dirac- Electron and Chilarity in Graphene sheets

Graphene is a newly realized two-dimensional (2D) electron system[1,2]which has engendered a great deal of interest because of the new physics which it exhibits and because of its potential as a new material for electronic technology. The agent responsible for many of the interesting electronic properties of graphene sheets is the non-Bravais honeycomb-lattice arrangement of carbon atoms, which leads to a gapless semiconductor with valence and conduction π bands.States near the Fermi energy of a graphene sheet are described by a massless Dirac equation which has chiral band states in which the honeycomb-sublattice pseudospin is aligned either parallel to or opposite to the envelope function momentum. The Dirac-like wave equationleads to both unusual electron-electron interaction effects and to unusual response to externalpotentials. Because of band chirality, the role of electron-electron interactions in graphene sheets differs in some essential ways[3,4] from the role which it plays in an ordinary 2D electron gas.