Theoretical study of (4.4) and (8.8) “armchair”-type carbon nanotubes in a strongly correlated electron model

Abstract

Background. Carbon nanotubes are widely used in practice; much attention is paid to theoretical studies of nanotubes, which make it possible to explain the unique physicochemical properties of nanotubes. Therefore, the research topic is very relevant. The purpose of this research is to study the energy spectrum, correlation function and density of electronic states of armchair carbon nanotubes (4.4) and (8.8), consisting of a finite number of atoms from 48 to 240 carbon atoms. Materials and methods. To study the features of the electronic structure of “armchair”-type carbon nanotubes of (4.4) and (8.8), consisting of the same number of carbon atoms, from a real nanotube for the possibility of a mathematical description within the framework of quantum field theory, we pass to the model of a nanotube, proceeding from the fact that in the case of nanotubes, the decisive role is played by π-electrons, they are responsible for electron transport. When setting the problem, we take into account the electron hopping from one site to the neighboring nanotube site. In addition, if there was already an electron at a neighboring site, when another electron appears, it becomes necessary to take into account the Coulomb repulsion of these two electrons with different spin projections. To solve this kind of problems, you can use the Hubbard model. Results. The anticommutator Green’s function is calculated, the equations of motion are derived, the energy spectra are constructed and analyzed, the correlation functions are determined for carbon nanotubes of the chair type (4.4) and (8.8) of 48, 96, 128, 160, 192 and 240 atoms. The density of electronic states is calculated for carbon nanotubes of 48, 96, 128, 160, 192, and 240 atoms. Conclusions. Analysis of a carbon nanotube’s study showed that with an increase in the number of atoms, the width of the lower and upper Hubbard subbands increases. The band gap between the Hubbard subbands decreases with the growth of the nanotube; the studied nanotubes behave like semiconductors. An increase in the number of atoms in a nanotube leads to a smoothing of the graph of the density of electronic states. The peaks in the density of electronic states correspond to the Van Hove singularity. Analysis of the graphs of the correlation function shows that the longer the nanotube, the better the conducting properties will be.

Keywords

• carbon nanotube
• green’s function
• correlation function
• energy spectrum
• chemical potential
• density of electronic states