Two nanotubes with different diameter and helicity can be connected without dangling bonds by introducing a pair of disclinations, a 5-membered ring and a 7-membered ring, in the honeycomb lattice of the nanotubes. (S.Iijima,et al., Nature 318, 162 (1985)) The nanotubes become metals and semiconductors according to their diameter and helicity. The junctions connecting two metallic nanotubes are considered. We calculated the Landauer's formula conductance by two methods, tight binding model and the effective mass approximation. The energy region |E| < Ec near the undoped Fermi energy E=0 is considered where the channel number is kept to two. The results by the two methods coincide with each other fairly well except when when |E| > 0.9Ec. ( R. Tamura and M. Tsukada, Phys. Rev. B 58, 8120 (1998) ) In the latter method, the closed analytical results about the conductance and the wave function can be obtained. From the wave function, we can explain the features of the conductance, e.g., resonant peaks as a function of the energies and power law decay as a function of the length of the junction. The discrepancy becomes, however, considerable when |E| > 0.9 Ec. The numerical results are compared with the corresponding analytical ones and the results show that the origin of the discrepancy comes from the evanescent waves with the longest decay length in the tube parts.
The band structures of the periodically connected nanotube junctions are also investigated by the same methods. Both methods show good agreement also in this system. The degeneracy and repulsion between the bands, which determine existence of the gap, are determined only from symmetries. The width of the gap and the band are in inverse proportion to the length of the unit cell. ( R. Tamura and M. Tsukada, J. Phys. Soc. Jpn.,68, 910 (1999) )
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