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