Local semiconducting transition in armchair carbon nanotubes: The effect of periodic bi-site perturbation on electronic and transport properties of carbon nanotubes

In carbon nanotubes, the most abundant defects, caused for example by irradiation or chemisorption treatments, are small perturbing clusters, i.e., bi-site defects, extending over both A and B sites. The relative positions of these perturbing clusters play a crucial role in determining the electronic properties of carbon nanotubes. Using band structure and electronic transport calculations, we find that in the case of armchair metallic nanotubes a band gap opens up when the clusters fulfill a certain periodicity condition. This phenomenon might be used in future nanoelectronic devices in which certain regions of single metallic nanotubes could be turned to semiconducting ones. Although in this work we study specifically the effect of hydrogen adatom clusters, the phenomenon is general for different types of defects. Moreover, we study the influence of the length and randomness of the defected region on the electron transport through it.

Figure 1

Three different hydrogen clusters—H2, H4, and H6 (blue circles)—used in the calculations. They are shown on a piece of an armchair SWCNT’s surface. The unit vectors of the graphene sheet ($\mathrm{a⃗}$ and $\mathrm{b⃗}$), the A and B sublattices, the Fermi wavelength (${\lambda }_F=3a$), and a vector connecting the adjacent hydrogen clusters are also given. The unit cell (UC) of the pristine tube with the length “a,” as well as superlattice unit cells corresponding to two different periodicities of the hydrogenated SWCNTs (SC5H4 and SC6H4), are shown.

Figure 2

Effect of the periodically repeated H4 clusters on the band structure of the (8,8) SWCNT. The band structure of (a) the pristine nanotube SC1H0 is compared to those for nanotubes with H-atom clusters and different supercell lengths, i.e., for (b) SC4H4, (c) SC5H4, and (d) SC6H4 (for the notation see the text and Fig. 1). “a,” on the wave vector axis, is the length of the CNT unit cell, as shown in Fig. 1. The dotted lines in (b)–(d) denote the band structure of the pristine nanotube folded according to the length of the supercell. The (blue) dashed lines in panel (a) are band or Brillouin zone folding lines for SC3H0. For any SC($3M$) with an integer $M$, these lines are two of the $3M-1$ folding lines. Therefore in all of these cases, the Fermi point is placed, after the folding, near the $\Gamma$ point.

Figure 3

Effect of the relative positions and the number of bi-site perturbations on the transmission coefficient of armchair SWCNTs. The (red) solid curves in the upper and lower rows show the tight-binding results for central regions $N$(SC5H4) and $N$(SC6H4), respectively. From left to right, $N=1$, 2, 5, and 10. The dotted black lines give the pristine transmission function. The dashed (green) curve in the lower left panel gives the DFT result calculated by the Transiesta program.

Figure 4

Fermi-energy transmission coefficient for $N$(SC6H2), $N$(SC6H4), and $N$(SC6H6) scattering regions as a function of $N$, the number of the perturbing supercells.

Figure 5

Fermi-energy transmission coefficient for different systems made by manipulating the original 10(SC6H4) system by displacing two of the H4 clusters. In the notation giving the sequence of the clusters, S and N stand for clusters Satisfying and Not satisfying the condition of Eq. (1). Sample results due to changing clusters’ positions (Disaligned) around the circumference perpendicular to the tube axis and due to replacing some of the H4 clusters by H6 or H2 clusters (Different Clusters) are also shown. The solid (red) line is the Fermi-energy transmission value for the original 10(SC6H4)system and the (black) dotted lines are, for comparison, those for the $N$(SC6H4) systems with $N=9$, 8, 7, and 6.