From graphene to graphite:: Electronic structure around the K point

Within a tight-binding approach we investigate how the electronic structure evolves from a single graphene layer into bulk graphite by computing the band structure of one, two, and three layers of graphene. It is well known that a single graphene layer is a zero-gap semiconductor with a linear Dirac-like spectrum around the Fermi energy, while graphite shows a semimetallic behavior with a band overlap of about 41 meV. In contrast to a single graphene layer, we show that two graphene layers have a parabolic spectrum around the Fermi energy and are a semimetal like graphite; however, the band overlap of 0.16 meV is extremely small. Three and more graphene layers show a clear semimetallic behavior. For 11 and more layers the difference in band overlap with graphite is smaller than 10%.