Relationship between cap structure and energy gap in capped carbon nanotubes.

Revealing a universal relation between geometrical structures and electronic properties of capped carbon nanotubes (CNTs) is one of the current objectives in nanocarbon community. Here, we investigate the local curvature of capped CNTs and define the cap region by a crossover behavior of the curvature energy versus the number of carbon atoms integrated from the tip to the tube region. Clear correlations among the energy gap of the cap localized states, the curvature energy, the number of carbon atoms in the cap region, and the number of specific carbon clusters are observed. The present analysis opens the way to understand the cap states.