Conductance of nanotube junctions and its scaling law

The conductance of junctions connecting two different metallic carbon nanotubes is calculated by Landauer's formula with a simple tight-binding model. The structures of the junctions are characterized by the relative positions of a pair of disclinations, i.e., a five-membered ring and a seven-membered ring. Conductances of about six thousand kinds of junctions are obtained. The conductance is determined only by the ratio ${\mathrm{R}}_2$/${\mathrm{R}}_1$ where ${\mathrm{R}}_1$ is the the circumference of the thinner tube and ${\mathrm{R}}_2$ is that of the thicker tube. When ${\mathrm{R}}_2$/${\mathrm{R}}_1$≫:1, the conductance is found to be almost proportional to (${\mathrm{R}}_2$/${\mathrm{R}}_1$ ${)}^{\mathrm{-}3}$. The wave function in the junction also shows a power-law decrease as a function of the distance measured from the thinner tube.