Tight-binding Results Research Articles

Electronic band structure and bonding in Nb3O3.

The local-density approximation is used to investigate the electronic and structural properties of ${\mathrm{Nb}}_{3}$${\mathrm{O}}_{3}$ and the reasons for its unusual defect rocksalt structure with 25% ordered vacancies. A tight-binding Hamiltonian is fitted to the energy bands which are compared to those of the hypothetical rocksalt phase. This analysis indicates that the ions in the ordered vacancy structure are nearly neutral, the Madelung energy is small, and electronic band effects contribute decisively to its stability. The tight-binding results are consistent with the interpretation that this structure favors a special hybridization between Nb d orbitals and their direct interaction gives rise to strong and nearly covalent metal-metal bonds. The formation of metallic bonds mainly between Nb p and Nb d orbitals around the O-vacancy site gives rise to the so-called ``vacancy band.''

Theory of oscillatory exchange in magnetic multilayers: effect of partial confinement and band mismatch

In an earlier work a theory of the oscillatory exchange coupling between two ferromagnetic layers across a nonmagnetic spacer was proposed. It relied on size-quantization of the energy of electrons of one spin confined in the spacer (complete confinement model). Detailed tight-binding calculations of the coupling between Fe layers across Cr(001) using five d orbitals and the complete confinement model are reported. The coupling exhibits oscillations with several different periods but the amplitude and phase do not agree with experiment. An exactly solvable hole gas model and new tight-binding results are presented which demonstrate that the oscillation period is unaffected but the amplitude and phase depend critically on the degree of confinement. In particular, the amplitude is reduced dramatically for a weak confinement appropriate to iron. The dependence of the coupling on the occupancy of the spacer layer d band is also investigated. It is shown that a mismatch between the ferromagnet and spacer layer d bands, which increases with increasing number of holes in the spacer, leads to a systematic variation of the coupling strength across the transition metal series in agreement with experiment.

Exchange coupling in magnetic multilayers: effect of partial confinement of carriers

The exchange coupling J(l) between magnetic layers across a non-magnetic spacer is observed to oscillate as a function of the spacer thickness l. In an earlier work a theory of the oscillatory exchange was proposed which shows that the oscillation periods are characteristic of the spacer. The theory relied on the assumption of an infinitely large exchange splitting in the magnetic layers, which leads to complete confinement of magnetic carriers of one spin in the ferromagnetic configuration of the sandwich. While this may be valid for strong ferromagnets such as Co or Ni, the complete confinement model is not a realistic approximation for iron which has holes in its majority-spin band. The theory is now generalized to the case of partial confinement of carriers in the spacer appropriate to a sandwich with weakly ferromagnetic layers. An exactly solvable hole-gas model of the coupling as well as numerical tight-binding results are presented which demonstrate that the oscillation period is unaffected but the amplitude and phase depend critically on the degree of confinement. Asymptotic expansions for J(l) valid at finite temperature and for an arbitrary single tight-binding band are also obtained. They show that the period and temperature dependence of the oscillations are directly related to the properties of the spacer Fermi surface but the amplitude and phase depend also on the exchange splitting in the ferromagnetic layers.

Tight-binding study of the lattice dynamics of graphite.

The vibrational spectrum of a two-dimensional (2D) sheet of graphite is examined using a tight-binding total-energy formalism. Motivation for this work is provided by the poor transferability of classical valence-force models for ${\mathit{sp}}^{2}$ carbon. A major problem with such models is the neglect of \ensuremath{\pi}-electron polarizability. The full tight-binding formalism considered here includes both this effect and covalent \ensuremath{\sigma} bonding on the same footing. Atomic force constants of arbitrary range are calculated quantum mechanically using a Green's-function approach. Long-range interactions, resulting from delocalized \ensuremath{\pi} bonding, are shown to be important for in-plane vibrations. The restoring forces for out-of-plane vibrations are dominated by \ensuremath{\sigma}-\ensuremath{\pi} mixing. The resulting phonon spectrum for 2D graphite is accurate only to within 30%. This is considerably worse than previous tight-binding results for ${\mathit{sp}}^{3}$ solids. Some possible reasons for this are discussed. The difficulties encountered here may well impede our ability to understand the vibrational properties of more complicated \ensuremath{\pi}-bonded solids, particularly amorphous carbons and fullerenes.

Near-threshold photoionization of nickel clusters: Ionization potentials for Ni3 to Ni90

The threshold photoionization efficiency (PIE) curves for nickel clusters in the size range Ni3 to Ni90 have been measured by laser photoionization with detection by time-of-flight mass spectrometry. Both warm (≤298 K) and cold (≤77 K) clusters have been studied. The PIE curves for 298 K clusters display thermal tails, while these tails are smaller for cold clusters. Cluster ionization potentials (I.P.s) have been determined by two methods: the Watanabe procedure and linear extrapolation of the PIE curves. Dramatic dependence of I.P. on cluster size is found for clusters smaller than 11 atoms, while the I.P.s of larger clusters decrease relatively smoothly and nearly monotonically from 5.84 eV for Ni11 to 5.56 eV for Ni90. The I.P.s for clusters larger than Ni40 show the linear dependence on reciprocal radius (R−1) predicted by the conducting spherical drop model of small particle I.P.s, but do not fit the model quantitatively unless the limiting (R−1→ 0) work function is reduced by 0.46 eV from the bulk polycrystalline value. The differences between the thermal tails of the room temperature and 77 K PIE curves diminish with increasing cluster size, suggesting a reduced difference between neutral and ionic structures for larger clusters. In general, there is poor agreement between our experimental results and theoretically calculated I.P.s for small nickel clusters, with the exception of the recently reported tight-binding theory results of Pastor et al. [Chem. Phys. Lett. 148, 459 (1988)].

Credibility of different calculational schemes for defects in semiconductors: their power and their limits

Two theoretical methods for calculating the electronic structure of point defects are reviewed critically: the empirical tight-binding approximation and local-density theory. The physical basis of the tight-binding approximation is recalled and the dispersion of tight-binding results is analysed for the case of vacancies in silicon and gallium arsenide. Some other points are also discussed such as the validity of the orbital removal method and the pinning of impurity states. The effects of correlation are then analysed: there are two main effects-multiplet splitting, whose local-density estimate is found to provide good agreement with experimental EPR data for vacancies in silicon, and shift in one-particle excitation energies with respect to local-density eigenvalues which is impossible to estimate accurately at the moment. It is concluded that both methods lead to errors of several tenths of an electron-volt as regards the prediction of the position of defect energy levels but nevertheless can provide useful information concerning other properties. Possible ways of improvement are outlined.

Conductivity of the disordered linear chain

The authors develop a fast algorithm for evaluating the Kubo formula for the conductivity of a linear chain, and use it to study the dependence of the conductivity as a function of imaginary frequency. The results for the Anderson model with different degrees of disorder and different energies can all be scaled onto the same curve, which is of the form expected from the theory of localised states. The universal curve obtained provides a simple connection between tight-binding model results and the conductivity which can be calculated for an electron in a white noise potential. Similar, but not identical, results are obtained for tight-binding chains with a Cauchy distribution of site energies.

Electronic structure of SnS2, SnSe2, CdI2and PbI2

The band structures of the layer compounds SnS2, SnSe2, CdI2 and PbI2 are calculated by the tight-binding method. They are in closer agreement with experimental results and previous pseudopotential calculations than previous tight-binding results have been. A universal band structure for the family is found by use of approximate algebraic band energies. For the 16-electron crystals a Gamma 2- to L1+ indirect gap and a main optical transition due to anion p-cation p orbitals is found, whilst for PbI2 the gap is direct at A.

Electronic energy-band structure of t r a n s-polyacetylene: EHCO and MNDO studies

Extended Hückel and MNDO programs developed for molecular systems have been modified without reparametrization to perform crystal orbital calculations. A comparison of the qualitative results of these methods with the extended tight binding results of Grant as applied to the band structure calculation of trans-polyacetylene is presented. It is demonstrated that the ETB, EHCO, and MNDO methods give results which show a similar trend with minor differences in detail. The usefulness of the crystal orbital method for the interpretation of experimental density of state curves of doped and undoped polymers is inferred from this study and previous studies on polyethylene.