The electronic structure of the transition metal dichalcogenide layer compounds is studied using hybridised orbitals appropriate to the transition metal atom coordination. Non-bonding orbitals on the transition metal atoms give the conduction electron bands which are responsible for the charge-density-wave phase transitions in the VB compounds, and the band structure of 1T- and 2H-TaS2 is found using tight binding. The phase transitions are studied by a tight-binding calculation of the conduction electron contribution to the dynamical matrix, Phi el. In 1T-TaS2 there is a Kohn anomaly in Phi el close to the displacement wavevector of the incommensurate phase, sufficiently large to make the ideal structure unstable. The ideal 2H structure is also unstable, though there is only a weak Kohn anomaly. As Phi el is fairly temperature independent, the stability of the high-temperature phase must be due to phonon entropy, and this is studied using a mean-field theory of anharmonic effects. The low-temperature commensurate phases are stabilised by chemical bonding effects.
We have performed surface electronic structure calculations for W(001) using the surfaceembedded Green function technique. These calculations enable us to interpret angle-resolved photoemission spectra, which play an important role in the controversy over the surface reconstruction of W(001). We show that the state which, according to most theories, plays a key role in driving the reconstruction is apparently invisible in the photoemission spectra, because of its in-plane character.
Plasmon modes of a two-dimensional lattice of long conducting circular wires are investigated by using an embedding technique to solve Maxwell's equations rigorously. The frequency-dependent density of states is calculated for various values of the wave vector and the filling fraction. At low filling fractions, collective modes are all found to accumulate at the surface-plasmon frequency ${\ensuremath{\omega}}_{p}∕\sqrt{2}$, ${\ensuremath{\omega}}_{p}$ being the bulk plasmon frequency. As the filling fraction increases, the interference between the electromagnetic fields generated by localized surface-plasmon polaritons leads to the presence of new resonances, whose frequency strongly depends on the interparticle separation. For touching wires, a number of multipole resonances fill the spectral range between dipole resonances, as occurs in the case of a three-dimensional packing of metal spheres.
A new method is developing for finding the quasiparticle density of states in an infinite system containing a region where electron-electron interactions occur. Density fluctuations in this region couple the Schrodinger equations for the components of a generalised quasiparticle amplitude. The method is applied to the Anderson model of an adsorbate, the discrete channels coupled by the density fluctuations being determined from a cluster calculation. The resulting densities of states are satisfactory for all strengths of coupling between the adsorbate and substrate, and electron-electron interaction.
A new Green function method for solving the Schrodinger equation for impurity A dissolved in B is applied to Mg in Li and Al in Li. In this method the Green function for A in B is expressed in terms of Green functions for bulk A and B and so it facilitates comparison with the atoms in the bulk. It is found that the local density of states outside the impurity goes quickly to the value for bulk B and inside the impurity it is close to the value for bulk A, except at low energies where it changes to allow for states in bulk A which are below the bottom of the B band. In the Al impurity case a weakly bound state falls out from the bottom of the band. The results are used in a discussion of charge densities, energies and sizes of impurities, and they show why a metal impurity in another metal largely retains its bulk properties.
The uniform surface contraction on Mo (001) and the phase transition observed below 300K are due to the peak in the surface density of states at the Fermi energy. This is essentially a virtual bound 4d state on the surface atoms, and contraction increases its interaction with the substrate and lowers the energy. The phase transition probably consists of a sideways displacement of the atoms which introduces new Brillouin zone boundaries broadening surface resonances at the Fermi energy.
The embedding method is a powerful theoretical and computational technique that is relevant to a great many technologically and scientifically important problems. This general nature encompasses many important and topical problems in for example surface and interface electronic structure, adsorption, physics of nanostructures, molecular electronics, plasmonics and photonics, and it has become an important tool for researchers in these fields. More recently it has also been extended into the time domain. Supplemented with demonstration programmes, code and examples, this book provides a thorough review of the method and would be an accessible starting point for graduate students or researchers wishing to understand and use the method, or as a single reference source for those already familiar with the subject and applying it in their research. Supplementary materials provided by the author to accompany the book are available within Book information.
Metallic perturbation theory is inadequate to explain the B-32 crystal structure of NaTl, LiAl, consisting of two interpenetrating diamond structures. However these compounds are probably semiconductors or semimetals, and an extra term must be included in the energy calculation to allow for the full Jones' zone. The structure can then be understood in solid state terms, which are related to the chemical picture of diamond-type bonds between the Tl atoms.
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