The kagomé net: Band theoretical and topological aspects

The Kagomé net (a two-dimensional hexagonal network comprising triangles and hexagons) is a building block of a number of intermetallic compounds. In order to understand the electronic characteristics of such an array of atoms, extended Hückel tight binding calculations have been performed on a Kagomé net of boron atoms. Comparisons have been drawn with other hexagonal nets, namely the graphite net and the close packed triangular net, and topological relationships between these nets are used to explain similarities in their band spectra. It is shown that simple Hückel theory can be used to obtain a rough estimate for the energies of the bands at specific high symmetry k-points, and a way of representing and evaluating energies of crystal orbitals with complex coefficients is discussed. A moments-based analysis of the relative energies of the three nets as a function of electron count is also presented. The effect on its band structure of trigonally distorting the Kagomé net is investigated. Finally, substituted ABC and AB2 derivatives of the Kagomé net are discussed.