Calculation of the spectral momentum density for electrons in a topologically disordered model of amorphous graphite

Abstract

The spectral momentum density (SMD) has been computed for electrons in a two-dimensional topologically disordered continuous random network (CRN) model of amorphous graphite, where odd-membered rings have destroyed all remnants of a crystalline lattice. The basis of this approach is an operator, referred to as the network momentum operator (NMO), constructed from the structural relationships of the CRN model: each atom is three-fold coordinated and is a member of only five-, six- or seven-membered rings. This operator generates a relationship between energy and momentum in an analogous way to that in which the translation operator does in crystalline materials. In particular, any Hamiltonian, H, for the disordered system can be separated into a conservative Hamiltonian, H0, which commutes with the NMO, and a potential, V, which only mixes states from different irreducible representations of the NMO. The potential V has been shown to be exponentially localized to the odd-membered rings in the CRN model, and therefore the NMO can be thought of as a mapping from topological to substitutional disorder. The SMD is computed using the conservative or effective medium Hamiltonian H0. The result is similar to a spherical average of the crystalline band structure for energy states close to the Δ point in the Brillouin zone of the crystalline material, but is qualitatively different for states closer to the Brillouin zone boundaries. The computed SMD is discussed in relation to results from inelastic electron scattering experiments on samples of evaporated and ion-sputtered amorphous carbon.