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The Landauer's formula conductance of the telescoped armchair nanotubes iscalculated with the Hamiltonian defined by first-principles calculations(SIESTA code). Herein, partially extracting the inner tube from the outer tubeis called 'telescoping'. It shows a rapid oscillation superposed on a slowoscillation as a function of discrete overlap length $(L-1/2)a$ with an integervariable $L$ and the lattice constant $a$. Considering the interlayerHamiltonian as a perturbation, we obtain the approximate formula of theamplitude of the slow oscillation as $|A|^2/(|A|^2+\varepsilon^2)$ where $A$ isthe effective interlayer interaction and $\varepsilon$ is the band splitwithout interlayer interaction. The approximate formula is related to theThouless number of the dispersion lines.

physical review. b, condensed matter and materials physics

Relation between dispersion lines and conductance of telescoped armchair  double-wall nanotubes analyzed using perturbation formulas and  first-principles calculations