Electronic Excitations in Carbon Nanostructures: Building-Block Approach

The description of nanostructures using a plane-wave basis set usually requires large supercells in order to avoid spurious Coulomb interactions between the replicas. In particular, the calculations of electron energy-loss spectra for low-dimensional systems like graphene or carbon nanotubes become numerically very demanding or even unfeasible. We overcome this problem by means of a building-block approach: Combining effective-medium theory and ab-initio calculations we can describe the collective excitations in nanostructures (like carbon nanotubes) starting from the microscopic polarisability of their building blocks (bulk graphite). To this end, Maxwell s equations are solved using the full frequency- and momentum-dependent microscopic dielectric function $\epsilon(q,q ,\omega)$ of the bulk material. The latter is calculated from first principles within the random phase approximation [1]. Besides an important gain in calculation time this method allows us to analyse the loss spectra of nanostructures in terms of their normal-mode excitations. We apply the building-block approach to study angular-resolved loss spectra for graphene and single-wall carbon nanotubes and find a very good agreement with full ab-initio calculations of these systems and corresponding experiments. Our findings can be also used for an efficient theoretical description of spatially-resolved electron energy-loss experiments. [1] AbInit: www.abinit.org, DP-code: www.dp-code.org