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

TL;DR

This study investigates how the conductance of telescoped armchair double-wall nanotubes varies with overlap length, using first-principles calculations and perturbation formulas to analyze oscillatory behavior and interlayer interactions.

Contribution

It introduces an approximate formula linking conductance oscillations to interlayer interaction and dispersion lines, combining first-principles calculations with perturbation theory.

Findings

Conductance exhibits rapid and slow oscillations with overlap length.

The amplitude of slow oscillation is approximated by a formula involving interlayer interaction.

The formula relates to the Thouless number of dispersion lines.

Abstract

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 $(L-1/2)a$ 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 $|A|^2/(|A|^2+\varepsilon^2)$ where $A$ is the effective interlayer interaction and $\varepsilon$ is the band split without interlayer interaction. The approximate formula is related to the Thouless number of the dispersion lines.