Abstract
The development from ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$ to an infinitely long tube is studied by changing the carbon number N. The extended Su-Schrieffer-Heeger Hamiltonian is applied to various geometrical structures and solved for the half-filling case of \ensuremath{\pi} electrons. For finite N (\ensuremath{\sim}100), appreciable dimerizations (\ensuremath{\sim}0.01 \AA{}) exist, and a fairly large gap (\ensuremath{\sim}0.1--1 eV) remains. The solution, which includes the perfect Kekul\'e structure, always gives the lowest energy. Other solutions, where there are deviations from the Kekul\'e structure, have higher energies. When N goes to infinity, the strength of the unique dimerization pattern, i.e., the perfect Kekul\'e structure, becomes too small to be observed, but the gap width (\ensuremath{\simeq}0.02 eV) is comparable to room temperature and can be measured. Therefore, the infinitely long tube will have properties like those of semiconductors with a very narrow gap. We would not expect perfect metallic properties, but peculiar properties due to the small gap could be observed in experiments.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call