Topological Defects in Carbon Nanocrystals

Abstract

The modern status of the problem of topological defects in graphitic nanocrystals is discussed. The gauge theory and topology are proved to be powerful methods in analyzing the electronic structure of variously shaped carbon nanoparticles. Both the eigenfunctions and the local density of states (DOS) near the pentagonal defects are calculated for three geometries: sphere, cone, and hyperboloid. It is found that the low-energy DOS has a cusp, which drops to 0 at the Fermi energy for any number of pentagons at the tip except 3. For three pentagons, the nonzero DOS across the Fermi level is formed.