Tight-binding Basis Research Articles

Density of states of metal alloys with random transfer integrals

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.

Theory of the Magnetic Susceptibility of Tetrahedral Semiconductors

The magnetic susceptibility of an intrinsic tetrahedrally coordinated semiconductor is calculated using a tight-binding basis and approximations appropriate to the bond-orbital model. The susceptibility associated with the valence electrons is found to separate into a diamagnetic Langevin component and a paramagnetic Van Vleck component, both of which are found to be proportional to the square of the bond length, and nearly cancel in the homopolar semiconductors. The Langevin term is found to be approximately independent of polarity while the paramagnetic component varies with polarity, ${\ensuremath{\alpha}}_{p}$, as ${(1\ensuremath{-}{{\ensuremath{\alpha}}_{p}}^{2})}^{\frac{3}{2}}$.