Electronic properties of polygonal defects in graphitic carbon sheets

Remarkable features of local density of states (LDOS) at a single $n$-membered ring defect $\mathrm{}(n=4,5,7,8\mathrm{})\mathrm{}$ in monolayered graphite are described. Based on the $n$-fold rotational symmetry at the center of the $n$-membered ring, the wave functions and the spectra of these systems are classified into $n$ kinds of components according to the character of the rotational symmetry group. Based on the analysis using this symmetry, the LDOS can be considered as broadened energy levels of the corresponding isolated $n$-membered ring molecule. The $n$-membered ring defect with the large-$n$ limit can be considered a screw dislocation in the graphite. The value of its LDOS approaches zero as the inverse of the logarithm of the energy at the band edges and at the band center.