Electron transmission through atom-contacted carbon nanotubes

The transmission through side-contacted single-wall carbon nanotubes is investigated within the Landauer-Bütikker formalism for arbitrary tubes, geometries of contacts, and energies of transmission (E) for the case of monoatomic contacts. An efficient method to calculate transmission within the tight-binding approach including curvature effects is devised allowing, in particular, for an analytical treatment of zigzag, armchair, and some chiral tubes. The transmission function is described as a superposition of the contributions from one-dimensional bands of all nanotube lines, each of them oscillating or/and decaying with the distance between the leads. We find five different types of antiresonances. Two of them arise from a destructive interference of the contributions from different nanotube lines when E is in the gap of semiconducting nanotubes and either are due to symmetry reasons or are accidental. A further two can show up at energies of Van Hove singularities originating from isolated singular points in 1D bands of nanotubes and can lead either to split or completely missing transmission peaks. The fifth one is related to the flat band in zigzag nanotubes at the energy of Van Hove singularity in graphene and results in zero transmission between carbon atoms belonging to different translational units in these tubes. A strong anisotropy of transmission in two opposite directions along the tube’s axis is found in the middle of the energy gap of semiconducting nanotubes, which reaches several orders of magnitude in zigzag tubes. The transmission at Van Hove singularities (when nonzero) is of the order of unity and decays at a large axial distance R between the leads as $R^{-2},$ similarly to monoatomic chains. The transmission in the band region of nanotubes shows two types of behavior depending on the divisibility by three of the difference between corresponding reduced nanotube indices $n^{\prime }-m^{\prime }.$ Close to the Fermi level the amplitude of the transmission function is independent from the chiral angle of the nanotubes and scales as an inverse square of their diameter.