Polymorphism of extended fullerene networks: Geometrical parameters and electronic structures

The morphology of fullerene networks can be widely extended by introducing heptagonal of octagonal rings, which produce a Gaussian negative curvature. Their presence makes it possible to form donut-, coil- and sponge-shaped networks of carbon atoms. We discuss the geometry of the polymorphous forms based on the net diagram method relative to a honeycomb lattice, and further study the electronic structures constructed by the network of pi electrons system. Special emphasis is put on how the geometrical parameters, which specify the relative arrangement of polygonal rings, control the electronic structures in the various extended-fullerene networks. In addition, we mention that the presence of a certain type of edge in fullerene network derives critical localized edge states at the Fermi level.