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 binds of junctions are obtained. The conductance is determined only by the ratio R(2)/R(1) where R(1) is the the circumference the thinner tube and R(2) is that of the thicker tube. When R(2)/R(1) much greater than 1, the conductance is found to be almost proportional to (R(2)/R(1))(-3). The wave function in the junction also shows a power-law decrease as a function of the distance-measured from the thinner tube.