Analysis of quantum conductance of carbon nanotube junctions by the effective mass approximation

TL;DR

This paper investigates quantum conductance in carbon nanotube junctions using the effective mass approximation, deriving an analytical formula that aligns well with tight binding model results and clarifies the underlying scaling law.

Contribution

It introduces an analytical approach based on the effective mass approximation to model conductance in nanotube junctions, providing insights into the scaling law and simplifying previous tight binding calculations.

Findings

Analytical conductance formula derived from effective mass theory.

Good agreement between analytical and tight binding model results.

Clarification of the physical origin of the conductance scaling law.

Abstract

The electron transport through the nanotube junctions which connect the different metallic nanotubes by a pair of a pentagonal defect and a heptagonal defect is investigated by Landauer's formula and the effective mass approximation. From our previous calculations based on the tight binding model, it has been known that the conductance is determined almost only by two parameters,i.e., the energy in the unit of the onset energy of more than two channels and the ratio of the radii of the two nanotubes. The conductance is calculated again by the effective mass theory in this paper and a simple analytical form of the conductance is obtained considering a special boundary conditions of the envelop wavefunctions. The two scaling parameters appear naturally in this treatment. The results by this formula coincide fairly well with those of the tight binding model. The physical origin of the scaling law is clarified by this approach.