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

The Landauer’s formula conductance of the telescoped armchair nanotubes is calculated with the Hamiltonian defined by first-principles calculations (SIESTA code). Herein, partially extracting the inner tube from the outer tube is called ‘telescoping’. It shows a rapid oscillation superposed on a slow oscillation as a function of discrete overlap length $(L-1\mathrm{/}2)a$ with an integer variable $L$ and the lattice constant $a$. Considering the interlayer Hamiltonian as a perturbation, we obtain the approximate formula of the amplitude of the slow oscillation as $\mathrm{\mid }A{\mathrm{\mid }}^2\mathrm{/}(\mathrm{\mid }A{\mathrm{\mid }}^2+{\epsilon }^2)$ where $A$ is the effective interlayer interaction and $\epsilon$ is the band split without interlayer interaction. The approximate formula is related to the Thouless number of the dispersion lines.