Electronic properties of amorphous systems describable by a pseudopotential with applications to amorphous Si

We have developed a theory for calculating the density of states for one-component amorphous systems composed of spherical pseudopotentials. We derive a self-consistent equation for the self-energy Γ(k,E) of the form ndΓ/dn=-V¯+nt(k,k,E)/S(0) where n is the density of atoms, V¯ is the average potential, and t(k,k,E) is the t matrix describing scattering from the average potential when a single atom is fixed at a point in space plus the modification of the self-energy (ΔΓ) in the region of the atom. We propose a model for ΔΓ, an approximation for t(k,k,E) and then solve the approximate equation Γ≃-V¯+nt(k,k,E)/S(0) for amorphous Si. We find extreme sensitivity to the form of the structure factor S(q) of the solid but we succeed in obtaining a deep minimum in the density of states at the Fermi energy (${\mathit{E}}_{\mathit{F}}$), indicating that the theory is along the right lines. We also generalize the argument to a two-component system and suggest a further refinement of an approximate form for t(k,k,E).