Diameter Dependence of Sub-Terahertz AC Response of Metallic Carbon Nanotubes with a Single Atomic Vacancy

Abstract

The sub-THz AC response of metallic single-walled carbon nanotubes (M-SWNTs) with a single atomic vacancy is investigated theoretically focusing on its diameter dependence. We find that the AC response behaves more capacitively in large-diameter M-SWNTs with a vacancy at the center of the SWNT in contrast to the diameter-independent AC response of a pristine M-SWNT showing the inductive response. This can be understood from the fact that the large-diameter M-SWNTs with a vacancy have more scattering states for electrons around the vacancy than the small-diameter ones. In addition, the threshold of vacancy position from the center of the SWNT, beyond which the inductive response appears regardless of the Fermi level position, is higher for large-diameter M-SWNTs than for small-diameter ones. Moreover, we find that the AC response depends strongly on tube diameter, but not on the type of tube, i.e., armchair or zigzag. #

Alternating current response of carbon nanotubes with randomly distributed impurities

“…In our previous studies, [16][17][18] we have clarified that electron scattering induces a capacitive response. Here, it should be noted that the electron scattering in these cases involves a decrease in the DC conductance, which is in sharp contrast with the present case of long-range impurity scattering.…”

“…10,11 In addition, we have also examined the influence of a single defect on the AC response, which strongly decreases the DC conductance, [12][13][14][15] and we have clarified that electron scattering by the defect state induces a capacitive response. [16][17][18] The effects of the kinetic inductance and electron backscattering on the AC response have been studied and understood for the above simple cases. However, it is unclear whether the findings obtained from such simple systems are sufficient to understand real systems, which are more complicated.…”

“…In this work, the impurity potential U imp is introduced in the scattering region, and we focus our attention on the linear AC response to V. Our calculation of the admittance is based on our previous investigations. 17,18 Figure 1 shows the tube-length dependence of the DC conductance and emittance of a (10,10) metallic CNT with impurity potentials of (a) d ¼ 0:1a; n c ¼ 1% and (b) d ¼ 1:5a; n c ¼ 1% for several potential strengths u imp . Here, the concentration of impurities in the CNT is represented by n c .…”

“…This suggests that there is a competition between two dominant factors that determine the emittance behaviors: the kinetic inductance, which contributes to the inductive response 4,6,8,9,18 and is proportional to the transport time of electrons, and the electron scattering, which leads to the capacitive response. [16][17][18] Based on this fact, we can understand the emittance responses as follows. When the CNT length is small (<200 nm), the effect of electron scattering is weak as can be observed in the DC conductance behaviors.…”

“…From these results, we can conclude that the AC transport behaviors for short-range impurity scattering can be understood in a manner similar to the cases of simpler systems examined in our previous investigations. 4,[16][17][18] We next examine the effect of long-range impurity scattering on the AC response. Figure 1(b) shows the AC response of (10,10) metallic CNTs with randomly distributed long-range impurity potentials.…”