ABSTRACT
Carbon has shown itself to be the most exible of atoms, crystallizing in divergent phases such as diamond and graphite, and being the constituent of the entire zoo of (locally) graphitic balls, tubes, capsules, and possibly negative curvature analogs of fullerenes, the schwartzites. We compare the various sp2bonded forms of carbon, and describe conditions that open or close the optical gap. We also explore topological disorder in three-coordinated networks including odd-membered rings in amorphous graphene, as seen in some experimental studies. We start with the Wooten-Weaire-Winer (WWW) models due to Kumar and Thorpe, and then carry out ab initio studies of the topological disorder. The structural, electronic, and vibrational characteristics are explored. We show that topological disorder qualitatively changes the electronic structure near the Fermi level. The existence of pentagonal rings also leads to substantial puckering in an accurate density functional simulation. The vibrational modes and spectra have proven to be interesting, and we present evidence that one might detect the presence of amorphous graphene from a vibrational signature.
