Relation between transmission rates and the wave functions in carbon nanotube junctions

Electron transmission and wave functions through junctions with a pair of a pentagonal defect and a heptagonal defect connecting two metallic carbon n anotubes are analyzed by the analytical calculation with the effective-mass equation. The energy region \E\<E-c is considered where the channel number is kept to two. Close relation between the transmission rate and the wave function is found; the transmission rate is given by the inverse squared ab solute value of the wave function. The dependence of the transmission rates on the energy and on the size of the junction is clearly explained by the nature of the wave function. Though the wave function and the transmission rate calculated by the tight-binding model agree well with the correspondin g analytical results by the effective-mass approximation, the discrepancy b ecomes considerable when \E\ similar or equal to E-c. To study the origin o f this discrepancy, an efficient numerical calculation method is developed with a generalized transfer matrix for the tight-binding model. Their numer ical results are compared with the corresponding analytical ones and the re sults show that the origin of the discrepancy comes from the evanescent wav es with the longest decay length in the tube parts.