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

TL;DR

This study explores the electronic and structural properties of fullerene tubules using an extended electron-phonon model, revealing conditions for metallic, semiconducting, and dimerized configurations based on lattice geometry and energy gaps.

Contribution

It introduces a detailed analysis of dimerization patterns and electronic structures in fullerene tubules considering various geometries with an extended Su-Schrieffer-Heeger model.

Findings

Kekulé structures tend to occur in gapless undimerized systems.

Large-gap systems favor chain-like distortions along the tubule axis.

Electronic properties range from nearly metallic to semiconducting depending on the gap.

Abstract

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.