The structure of the π -band of graphite

Abstract

A three-dimensional tight-binding model of graphite, based on the 2 p z atomic orbital of carbon, is used to calculate the energy of the π conduction states near the Fermi surface. The results of a group-theoretical analysis of the problem are used to simplify the calculation. The energy is obtained as a four-valued function of the k-vector within a primitive unit cell in the reciprocal lattice. It is found that the first and second of these bands of states are almost fully occupied, while the third and fourth are almost empty. The lowest energy of the third band is about 4 x 10 -3 eV below the highest energy of the second band, so there are ‘free’ electrons even at absolute zero. Explicit formulae are given for the energy of the states within the region occupied by the Fermi surface at temperatures below 100° K . For temperatures above 100° K , or if electron traps are present, the energy distribution within the region occupied by the Fermi surface is tabulated in detail. This knowledge of the conduction states of graphite is used in a subsequent paper to calculate the Hall coefficient of a single crystal of graphite and is found to give good agreement with experiment.