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Register a new userMicroscopic Electronic Wavefunction and interactions between quasi particles in Empirical Tight-Binding Theory
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A procedure to obtain single-electron wavefunctions within the tight-binding formalism is proposed. It is based on linear combinations of Slater-type orbitals whose screening coefficients are extracted from the optical matrix elements of the tight-binding Hamiltonian. Bloch functions obtained for zinc-blende semiconductors in the extended-basis spds* tight-binding model demonstrate very good agreement with first-principles wavefunctions. We apply this method to the calculation of electron-hole exchange interaction, and obtain the dispersion of excitonic fine structure of bulk GaAs. Beyond semiconductor nanostructures, this work is a fundamental step toward modeling many-body effects from post-processing single particle wavefunctions within the tight-binding theory.
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A method for incorporating electromagnetic fields into empirical tight-binding theory is derived from the principle of local gauge symmetry. Gauge invariance is shown to be incompatible with empirical tight-binding theory unless a representation exists in which the coordinate operator is diagonal. The present approach takes this basis as fundamental and uses group theory to construct symmetrized linear combinations of discrete coordinate eigenkets. This produces orthogonal atomic-like orbitals that may be used as a tight-binding basis. The coordinate matrix in the latter basis includes intra-atomic matrix elements between different orbitals on the same atom. Lattice gauge theory is then used to define discrete electromagnetic fields and their interaction with electrons. Local gauge symmetry is shown to impose strong restrictions limiting the range of the Hamiltonian in the coordinate basis. The theory is applied to the semiconductors Ge and Si, for which it is shown that a basis of 15 orbitals per atom provides a satisfactory description of the valence bands and the lowest conduction bands. Calculations of the dielectric function demonstrate that this model yields an accurate joint density of states, but underestimates the oscillator strength by about 20% in comparison to a nonlocal empirical pseudopotential calculation.
For a previously published study of the titanium hcp (alpha) to omega (omega) transformation, a tight-binding model was developed for titanium that accurately reproduces the structural energies and electron eigenvalues from all-electron density-functional calculations. We use a fitting method that matches the correctly symmetrized wavefuctions of the tight-binding model to those of the density-functional calculations at high symmetry points. The structural energies, elastic constants, phonon spectra, and point-defect energies predicted by our tight-binding model agree with density-functional calculations and experiment. In addition, a modification to the functional form is implemented to overcome the collapse problem of tight-binding, necessary for phase transformation studies and molecular dynamics simulations. The accuracy, transferability and efficiency of the model makes it particularly well suited to understanding structural transformations in titanium.
The electronic structure is found to be understandable in terms of free-atom term values and universal interorbital coupling parameters, since self-consistent tight-binding calculations indicate that Coulomb shifts of the d-state energies are small. Special-point averages over the bands are seen to be equivalent to treatment of local octahedral clusters. The cohesive energy per manganese for MnO, Mn2O3, and MnO2, in which manganese exists in valence states Mn2+, Mn3+, and Mn4+, is very nearly the same and dominated by the transfer of manganese s electrons to oxygen p states. There are small corrections, one eV per Mn in all cases, from couplings of minority-spin states. Transferring one majority-spin electron from an upper cluster state to a nonbonding oxygen state adds 1.67 eV to the cohesion for Mn2O3, and two transfers adds twice that for MnO2 . The electronic and magnetic properties are consistent with this description and appear to be understandable in terms of the same parameters.
An earlier analysis of manganese oxides in various charge states indicated that free-atom term values and universal coupling gave a reasonable account of the cohesion. This approach is here extended to LaxSr(1-x)MnO3 in a perovskite structure, and a wide range of properties, with comparable success, including the cohesion, as a function of x. Magnetic and electronic properties are treated in terms of the same parameters and the cluster orbitals used for cohesion. This includes an estimate of the Neel and Curie-Weiss temperatures for SrMnO3, an antiferromagnetic insulator, and the magnitude of a Jahn-Teller distortion in LaMnO3 which makes it also insulating with (100) ferromagnetic planes (due to a novel double-exchange for the distorted state), antiferromagnetically stacked, as observed. We estimate the Neel temperature and its volume dependence, and the ferromagnetic Curie-Weiss temperature which applies between the Neel and Jahn-Teller temperatures. We expect hopping conductivity when there is doping (0<x<1) and estimate it in the context of small-polaron theory. It is in accord with experiment between the Neel and Jahn-Teller temperatures, but below the Neel temperature the conduction appears to be band-like, for which we estimate a hole mass as enhanced in large-polaron theory. We see that above the Jahn-Teller temperature LaMnO3 should be metallic as observed, and paramagnetic with a ferromagnetic Curie-Weiss constant which we estimate. Many of these predictions are not so accurate, but are sufficiently close to provide a clear understanding of all of these properties in terms of a simple theory and parameters known at the outset. We provide also these parameters for Fe, Co, and Ca so that formulae for the properties can readily be evaluated for similar systems.
We extend a tight-binding total energy method to include f-electrons, and apply it to the study of the structural and elastic properties of a range of elements from Be to U. We find that the tight-binding parameters are as accurate and transferable for f-electron systems as they are for d-electron systems. In both cases we have found it essential to take great care in constraining the fitting procedure by using a block-diagonalization procedure, which we describe in detail.
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