The effect of the mixing of π -and σ -orbitals on the Fermi surface in the l.c.a.o. model for graphite

Abstract

The common energy of the two principal conduction bands in graphite along the triad axes in k-space is recalculated using an l.c.a.o. model based on sixteen orbitals per unit cell; four 2 s and 2 p ( π and σ ) orbitals centred on each of the four atomic sites in the unit cell. (An earlier calculation took account only of the four 2 p z orbitals.) The results of a group-theoretical analysis are used to show that only 15 of the 136 elements of the resulting 16 x 16 secular determinant are required to compute the doubly degenerate root corresponding to the common energy of the two conduction bands on the triad axes. This energy is found to vary periodically along the triad axes with an amplitude of 0.013 eV. The corresponding overlap of the two conduction bands is about three times larger than the overlap found in the earlier calculation. The resulting correction to the energy surfaces near the triad axes is too small to affect the calculation of the Hall coefficient of graphite for room temperatures based on the earlier calculation, but it is significant at low temperatures. For temperatures below about 50° K and in the absence of electron donors or traps, the conduction region in k-space is confined to the top of the lower conduction band where the density of states per unit energy range is estimated to be 1.1 x 10 -2 √(0.0135 — ϵ ) electronic states per atom per electron-volt, and to the bottom of the upper conduction band where the density of states is found to be 5.8 x 10 -2 √ ϵ . Formulae are given for the shape of the energy surfaces in these regions.