Electronic transport and Fano resonance in carbon nanotube ring systems

The conductance and the local density of states in the ringlike intramolecular junctions composed of the single walled carbon nanotubes are investigated by using the tight-binding model and the Green’s function method. It is found that the Fano resonances emerge in the conductance plots of the systems due to the interference of the extended propagating modes and the defect states or the standing wave states. The asymmetrical topological defect distribution has a large influence on the transport of the system, broadening the quasibound states and making their coupling with the propagating modes stronger. When the two arm tubes forming the ringlike junction have different diameters, the smaller one more easily induces the standing wave states at some energies. The curvature effects, including the $\sigma \text{−}\pi$ hybridization have also been carefully studied, and are found to be able to induce remarkable changes of the quasibound states and the conductance of the system, e.g., the appearance of the near zero conductance within a certain energy range, indicating the transport state of the ringlike junction can be switched on and off by tuning the gate voltage.

Figure 1

Schematic view of the SWNT rings. The black balls represent the defect atoms. Model (a) formed by $(12,12)\text{−}(6,6)∕(6,6)$ tubes with six symmetrically distributed heptagons at each junction center, and three mirror symmetry planes of ${\sigma }_c$, ${\sigma }_p$, and ${\sigma }_i$, where ${\sigma }_i$ means the one perpendicular to both ${\sigma }_c$ and ${\sigma }_p$, and passing through the tube axis. Model (b) made out of $(12,12)\text{−}(5,5)∕(7,7)$ tubes with six symmetrically distributed heptagons at each junction center and two mirror symmetry planes of ${\sigma }_p$ and ${\sigma }_i$. Model (c) made out of $(12,12)\text{−}(6,6)∕(6,6)$ tubes with six asymmetrically distributed heptagons at one junction center, without mirror symmetry. The structure is relaxed with the universal force field (UFF) (Ref. 25).

Figure 2

The LDOS and conductances of all models for $\pi$ orbital only. In each subfigure, the top one corresponds to the LDOS, and the bottom one to the conductance. Insets: The amplified quasibound states at $E=-0.4365\mathrm{eV}$ for model (a) and conductance at $E=-0.1851\mathrm{eV}$ for model (b).

Figure 3

(Color online) 2D contour maps of the LDOS at some energies from $\pi$ orbital-only calculations. The A and B plots correspond to model (a) at $E=-0.5825$ and $0.4360\mathrm{eV}$, respectively. The C and D plots are for model (b) at $E=-0.5865$ and $0.4400\mathrm{eV}$, respectively. The atomic positions are marked by small circles. The $x,y$ axes are parallel and perpendicular to the $(12,12)$ tube axis, respectively.

Figure 4

The four-orbital results for the LDOS and conductances of (a) model (a), (b) model (b), and (c) model (c). Here, the $\pi$-orbital results have also been included for comparison.