Conductance gap and zero-bias conductance scaling in metallic carbon nanotubes

A new supercell approach is presented to the calculations for quantum conductance of single-wall carbon nanotubes as a function of tube length L, diameter d, and chirality. It is shown that there is a conductance gap ( dip) in infinite ( finite) metallic non-armchair nanotubes due to the curvature-induced energy gap, while it is absent in armchair tubes. This mediates a dispute in experiments. A scaling of G = 2G(0) exp[-beta L/d(2)] is obtained for the zero-bias conductance where G(0) = 2e(2)/h and beta depends only on the chiral angle. This behavior can be well understood by a proposed tunneling model.