Thermodynamic properties of nanotubes of triangular lattice

Abstract

The carbon nano-structures, known as nanotubes, are cylindrical structures that can be visualized as a rolled two-dimensional honeycomb lattice. The structural parameters strongly influence the transport properties of nanotubes. In this work we develop a mathematical expression for the calculation of the electric conductivity, and we calculate the density of states and determine several thermodynamic properties of a nanotube created from a triangular lattice. The thermodynamic properties such as mean energy, specific heat, magnetic susceptibility, magnetization, and electric conductivity, have been obtained using the Hubbard model with the technique of the equation of motion of the real time Green function. The results show that the nanotube with four sites in the perimeter (m = 4) present a  ferromagnetic-paramagnetic transition at Tc = 1,02 kB/t with U/t = 8. This work also shows that the initial critical value of U/t from which nanotube presents magnetization depends on the number of sites of the perimeter (m), that is, on the nanotube diameter, and from m = 50 on this critical interaction is equal to the value of the critical U/t of the triangular lattice, that is Uc/t ~ 5.5. From m = 50 on the nanotube also stops to present non-saturated ferromagnetism and the magnetization is satured. There is superconductivity in the nanotube and in the triangular lattice itself up to temperatures Tcs = 0.4 kB/t and Tcs = 0.6 kB/t, respectively. Above these temperatures the two systems present metallic behavior.