Field-theoretical approach to the description of electronic properties of carbon nanostructures

Discovery of new microcrystalline forms of carbon with a number of unique properties has required development of new approaches to the theoretical description of their electronic structure. The basic structure for the entire family of carbon nanostructures is a graphite sheet (graphene) whose electronic properties at the energy close to the Fermi energy are described using the field-theoretical approach. Other types of carbon nanostructures, such as fullerenes, open and closed nanotubes, nanocones, and nanohorns can be treated as modifications of the basic structure arising from the introduction of topological defects (disclinations) in it. In the field-theoretical approach, a tetradic formalism is introduced to take into account curvature of the surface, and gauge fields of two types are introduced to take into account presence of disclinations. The field-theoretical gauge formalism is used to study the behavior of the density of states for carbon nanocones, nanohorns, closed carbon nanotubes, hypothetical one-sheet hyperboloid nanostructures, and icosahedral (Ih) fullerenes (for which the energy spectrum and eigenfunctions are also studied).