Electronic structure of gold chirality nanotubes (5.0) in the Hubbard model

Background. The experimental and theoretical study of nanotubes made of gold atoms is currently being given great attention due to the great potential of their application in various fields: materials science, catalysis, modern electronics, and antitumor medicine. The aim of this work is a comparative study of the electronic structures of open and closed gold nanotubes (5.0) consisting of a finite number of Au atoms (from 45 to 257) as the length of the gold nanotube increases. Materials and methods. To describe the gold structure of gold nanotubes in the framework of the Hubbard Hamiltonian, a model is proposed in which the Au atoms are represented as the Au$^{+}$ ion, around which the d-electron moves, which is responsible for the transport properties in nanotubes. In nanotubes, d-electrons can jump from one atom to a neighboring atom because the wave functions of neighboring atoms overlap. If, as a result of an electron jump, there are two d-electrons at the same node, it is necessary to take into account the energies of their Coulomb interaction. The d-electron system of nanotubes made of Au atoms is a strongly correlated system. Results. The Fourier images of the Green's anticommutator function are calculated, the poles of which determine the spectrum of elementary excitations of the considered nanostructures made of Au atoms. The density of the electronic state of the quantum systems under study is determined, and an equation for the chemical potential for each nanostructure under study is obtained. The electronic structures of open and closed gold nanotubes are compared, and the electronic structures of gold atom nanotubes change as the number of atoms in the nanotube changes. Conclusions. From the studies, it can be concluded that as the length of the nanotube increases, the width of the band gap decreases. Both open nanotubes and closed nanotubes made of Au metal atoms, studied in this work, have semiconductor properties. The addition of two atoms (nodes) covering the nanotube leads not only to the appearance of an additional level of energy, but also to the restructuring of the entire spectrum. As the size of the nanotube increases, the effect of the “caps” on both the rearrangement of the energy spectrum and the density of the electron state gradually decreases. The gap width of the bandgap zone gradually tends to zero as the nanotube grows, when the number of atoms in the nanotube becomes about 250. In the course of the dependence graphs in Figure 2, we predict that with the growth of gold nanotubes (5.0), there is only a semiconductor-metal transition without the transition phenomenon with an increase in the length of the nanotube back to the semiconductor state, as follows from the work of X.P. Yang and J.M. Dong (2005).