Effects of Different Junction Parameters on Junction Conductances of Crossed Metallic Carbon Nanotubes

We have studied the effect of different junction parameters on the junction conductances made of two crossed metallic carbon nanotubes. We have found that because of the intrinsic asymmetries of the junction, forward and backward tunneling between one tube and the other are unequal. Passing a current in one tube leaded to the development of non zero voltage across the other one, a zero field Hall like conductance for the junction was found. We have found that this zero field Hall conductance relates to the contact conductance of the junction. The result also shows that the electronic properties of the junction sensitively depend on the degree of matching between the tube lattices. This matching is controlled by the crossing angel, which resulted in an intertube conductance that varied by an order of magnitude for different angles. We have derived a tunneling matrix element that coupled the low energy electronic states on the two tubes. The magnitude of the coupling was determined by the intertube separation of the crossing angle. We have found that the intrinsic symmetries of the junction created a discrepancy between the forward and backward hopping between the tubes. Using Landauer-Buttiker formalism, we have calculated the different conductances of the four terminal junctions. We have found that the contact conductance scaled inversely with the zero field Hall conductance of the junction. We have also found that the two crucial parameters in determining the conductance are the tube chiralities and the crossing angle. The obtained results were found in good agreement with previously obtained results.