The “rule of multiplicity of three”: Does it work in carbon nanotubes?

ABSTRACT

The rule of multiplicity of three according to which a nanotube has a metallic conductivity if the difference between the chiral indices is a multiple of three or behaves as a semiconductor or dielectric in the opposite case, is commonly used for interpretation of the physical properties of carbon nanotubes (CNTs). This rule is shown to have limited validity, for example, for single-walled CNTs considered as strongly correlated systems in terms of the perturbation theory, in which the state of individual atoms is a zero approximation and the electron site-to-site hopping is regarded as a perturbation. Due to a strong Coulomb interaction between π-electrons at one site, the energy spectrum is divided into two Hubbard subbands resulting in conditions when the rule of multiplicity of three does not work.

KEYWORDS:

• Carbon nanotubes
• Hubbard model
• Density of states
• Optical spectrum

Acknowledgments

The work was conducted within the framework of Program of Fundamental Scientific Research of State Academies of Sciences for 2013–2020 with partial financial support of the Institute of Strength Physics and Materials Science SB RAS Improvement Program and grant of the Russian Foundation for Basic Research (no. 16-32-50015).