Density of states of metal alloys with random transfer integrals

Abstract

The electronic density of states of a binary alloy is calculated by applying the coherent-potential-approximation (CPA) method to a single-band model Hamiltonian that includes diagonal and off-diagonal random elements in a tight-binding basis. The theory deals with clusters consisting of a central atom plus its nearest neighbors. The CPA analysis can be carried through in the low-concentration limit. Numerical results are presented for the irreducible elements of the self-energy matrix (there are six for a simple-cubic alloy), and for the density of states of a simple-cubic dilute alloy. The band tails are found to depend sensitively on differences between the transfer integrals from an impurity to a host atom ${h}^{\mathrm{AB}}$ and that from one host atom to another ${h}^{\mathrm{BB}}$. When ${h}^{\mathrm{AB}}>{h}^{\mathrm{BB}}$ the band tails lengthen so impurity states are more localized, while in the opposite case, ${h}^{\mathrm{AB}}<{h}^{\mathrm{BB}}$, the tails are shortened so that impurity states are more extended. A generalization of the average $t$-matrix approximation (ATA) and its iteration (IATA) is formulated in the cluster basis. IATA facilitates numerical evaluations of the self-energies for highly concentrated alloys.