Dimerization and Energy-Level Structures in Fullerene Tubules Investigated with an Electron-Phonon Model

Possible dimerization patterns and electronic structures in fullerene tubules as the \pi-conjugated systems are studied with the extended Su-Schrieffer- Heeger model. We assume various lattice geometries, including helical and nonhelical tubules, and tubules with end caps. The model is solved for the half-filling case of \pi-electrons. (1) When the undimerized systems do not have a gap, the Kekul\'{e} structures tend to occur. These structures are commensurate with the boundary condition in the direction perpendicular to the tubular axis. The energy gap is of the order of the room temperatures at most. Thus, the nearly metallic properties would be expected. (2) If the undimerized systems have a large gap (\sim 1eV), the most stable structures are the chain-like distortions where the direction of the arranged {\sl trans}-polyacetylene chains is along almost the tubular axis. When we try to obtain the Kekul\'{e} structures, the mismatch of the boundary condition occurs and they are energetically unfavorable. The electronic structures are of semiconductors due to the large gap.