DYNAMICS AND SPECTRAL PROPERTIES OF FREE-STANDING NEGATIVELY-CURVED CARBON SURFACES

The growing interest for the physical properties of graphene and its chemical functionalization is triggering a renewed attention to other more complex forms of sp(2) nanostructured carbon, e.g., carbon schwarzites. The structural complexity of these forms prevents in many cases the possibility of ab-initio calculations of their electronic and vibrational properties. On the other hand in systems with a certain level of conjugation many of these properties depend primarily on the topological features of the structure - notably on the graph describing the bonding network and the associated adjacency matrix. In this work, specifically devoted to planar schwarzites, it is shown that their vibrational spectrum as obtained from the diagonalization of the adjacency matrix (topological phonons) reflects the main features of ah-initio calculations. Thus the method is suitable to the study of thermodynamic and spectral phonon properties of defective schwarzites which involve integrals over the unperturbed phonon density of states. Calculations of the phonon density of states smallest planar schwarzites and the effects of various type of local perturbation are presented and thoroughly discussed.