Quasi-Particle Spectra on Substrate and Embedded Graphene Monolayers

Graphite, graphene, and compounds based on them are of great interest both as objects of fundamental research and as some of the most promising materials for modern technologies. The two-dimensional form of graphite – graphene was prepared only very recently, immediately attracting a great deal of attention. Graphene can be deposited on solid substrates and has been shown to exhibit remarkable properties including large thermal conductivity, mechanical robustness and two-dimensional electronic properties. Note that electrons in graphene obey linear dispersion relation resulting in the observation of a number of very peculiar electronic properties. These properties are essentially changed when different defects are introduced into material. Special interest is devoted to graphite intercalated by metals, since in such graphitic systems the temperature of superconducting transition essentially depends on the type of intercalating metal. Besides, the discovery of superconductors as MgB2 and iron pnictides intensified the search for high-temperature superconductivity in materials other than copper oxides. It is known that in the formation of the superconducting state the electron-phonon interaction plays a crucial role (according to the Bardeen-Cooper-Schrieffer theory). Therefore it is necessary to analyze in detail the phonon spectra of pure graphite and to find out how these spectra are influenced by different defects and by intercalation. This chapter consists of three sections. The first section is devoted to the calculation of the local electronic density of graphene containing a substitutional impurity, vacancy defects due to the substrate surface roughness and adsorbed atoms. The local densities of states for atoms of the sublattice which not contains the vacancy show sharp peaks at energy F e e = ( F e is the energy of the Dirac singularity for ideal graphene). Local spectral densities of atoms of the sublattice which contains the vacancy conserve the same Dirac singularity as is observed in an ideal graphene. The second section will present our model, which allows to quantitatively describe the phonon spectrum of graphite and to determine the relaxation of force constants for the formation of the surface of the sample and the formation of thin films (bigraphene,