Fractal carbon clusters modelling new forms of carbon

Abstract

We propose a new form of carbon in which the atoms are arranged in a self-similar fashion. The hypothetical structure we consider is two-dimensional, having a fractal dimension d f = 1 + log 2 log 3 ≈ 1.63 which we call the Davidene. Our results for the ground state geometries of the aggregate as a function of its size L indicate that the fractal cluster is stable, displaying a small “gap” (≈ 0.16 eV) for large L. A detailed analysis of the energy spectrum shows that it possesses self-similar properties with a fractal dimension d f = 0.79 ± 0.02 for large L.