Perturbation calculations on interlayer transmission rates from symmetric to antisymmetric channels in parallel armchair nanotube junctions

Abstract

Partially overlapping two parallel armchair nanotubes are investigated theoretically with the $\pi$ orbital tight bonding model. Considering the interlayer Hamiltonian as perturbation, we obtain approximate analytical formulas of the interlayer transmission rates $T_{{\sigma }^{\prime },\sigma }$ from channel $\sigma$ to ${\sigma }^{\prime }$ for all the four combinations $({\sigma }^{\prime },\sigma )=(\pm ,\pm )$ and $(\pm ,\mp )$, where suffixes $+$ and $-$ represent symmetric and anti-symmetric channels, respectively, with respect to the mirror plane of each tube. Landauer's formula conductance is equal to the sum of them in units of $2e^2/h$. According to the perturbation calculation, the interlayer Hamiltonian is transformed into the parameter $w_{{\sigma }^{\prime },\sigma }$ that determines the analytical formula of $T_{{\sigma }^{\prime },\sigma }$. By comparison with the exact numerical results, the effective range of the analytical formulas is discussed. In the telescoped coaxial contact, the off-diagonal part $T_{-,+}+T_{+,-}$ is very small compared to the diagonal part $T_{+,+}+T_{-,-}$. In the side contact, on the other hand, the off-diagonal part is more significant than the diagonal part in the zero energy peak of the conductance.

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