Conductance of telescoped double-walled nanotubes from perturbation calculations

In a telescoped double-walled nanotube (TDWNT), with the inner tube partially extracted from the outer tube, the total current is forced to flow between the layers. Considering the interlayer Hamiltonian as a perturbation, we can obtain an analytic formula for the interlayer conductance. The accuracy of the perturbation formula is systematically improved by including higher-order terms. The interlayer interaction effective in the perturbation formula is the product of the interlayer Hamiltonian and the wave function. It clarifies the effects of the spatial range of the interlayer Hamiltonian and the band energy shift.