Diamond, graphite, graphene, and fullerenes are materials that although they only have carbon atoms, they have extremely different properties. One striking characteristic is that their bonding structure can be described as three-dimensional, two-dimensional and zero-dimensional. (And buckytubes and polyynes can be described as one-dimensional.) Their electronic structure has been calculated with density functional theory, will be interpreted with the help of simple tight-binding and nearly free electron models, and the connection between the properties of the materials and the electronic structure will be discussed. An important task is to find the band edges or the Fermi surfaces in the Brillouin zone, but even for these "simple" materials it may not be trivial. For complex materials it can be quite hard to identify the relevant features, and one needs a faster way to sample the whole Brillouin zone. The recent developed modified tight-binding method allows an interpolation of the bands in the whole Brillouin from a few points on a sparse grid. The same can be achieved by a Generalized Langreth-Kohn method related to the k.p approximation. These methods will be illustrated by applications to the carbon materials and to more complex materials such as semiconductor superlattices.

Organized by: Paulo Brás, Paulo Silva, Jaime Silva