Electron transmission through atom-contacted carbon nanotubes

Abstract

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 ͑E͒ 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 onedimensional 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 nonzero͒ is of the order of unity and decays at a large axial distance R between the leads as R Ϫ2 , 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 nЈϪmЈ. 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.

Eigenstates and transmission coefficients of finite-sized carbon nanotubes

“…The same conclusion has been reached for side-contacted infinite nanotubes. 28 We had seen before that for the three kinds of tubes, with n even, there was a high degeneracy at energy Ϯ␤ 1 , due to the eigenvalues of H Z (/2). The term T Z (/2 ,N) becomes…”

“…In other words, at the Fermi level the Green's function and as a consequence all properties derived from it are solely determined by the decaying wave function. The Green's function of the system with leads can be calculated from the Green's function of the isolated system making use of Dyson's equation 27,28 Gϭ͑IϪG 0 ⌺ ͒ Ϫ1 G 0 , ͑86͒ so we get…”

“…A similar behavior of the transmission was found in sidecontacted infinite armchair nanotubes. 28 In Fig. 5͑b͒ the transmission is plotted.…”

Electron transport in crossed nanotubes with a point contact

“…[21][22][23][24][25][26][27] The transmission through atom-contacted single-walled carbon nanotubes was calculated within the tight-binding approach. 21 Multiterminal junctions of single-walled carbon nanotubes were investigated using the classical molecular dynamics method. 22 Tight-binding calculations of the conductance of multiply connected metallic carbon nanotubes were carried out in Refs.…”

Kekulé pattern on conductance images between two STM probes

“…Topographical STM images have been calculated within a tight-binding model and the appearance of the honeycomb structure has been demonstrated in infinitely long nanotubes [8]. Electron transmission has been studied between two STM tips as leads which contact the nanotube via single carbon atoms [9]. Recently, we have shown a Kekulé type pattern in two-probe STM images in armchair carbon nanotubes due to interference of states at K and K' point except in special cases [10].…”