FROM C-60 TO A FULLERENE TUBE - SYSTEMATIC ANALYSIS OF LATTICE AND ELECTRONIC-STRUCTURES BY THE EXTENDED SU-SCHRIEFFER-HEEGER MODEL

The development from C60 and C70 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 pi-electrons. For finite N (approximately 100), appreciable dimerizations (approximately 0.01 angstrom) exist, and a fairly large gap (approximately 0.1-1 eV) remains. The solution, which includes the perfect Kekule structure, always gives the lowest energy. Other solutions, where there are deviations from the Kekule structure, have higher energies. When N goes to infinity, the strength of the unique dimerization pattern, i.e., the prefect Kekule structure, becomes too small to be observed, but the gap width ( congruent-to 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.