Defective transport properties of three-terminal carbon nanotube junctions

We investigate the transport properties of three-terminal carbon-based nanojunctions within the scattering matrix approach. The stability of such junctions is subordinated to the presence of nonhexagonal arrangements in the molecular network. Such “defective” arrangements do influence the resulting quantum transport observables, as a consequence of the possibility of acting as pinning centers of the corresponding wave function. By investigating a fairly wide class of junctions we have found regular mutual dependences between such localized states at the carbon network and a striking behavior of the conductance. In particular, we have shown that Fano resonances emerge as a natural result of the interference between defective states and the extended continuum background. As a consequence, the currents through the junctions hitting these resonant states might experience variations on a relevant scale with current modulations of up to 75%.

Figure 1

Four junctions entirely built up with semiconducting (10,0) and metallic (6,6) CNT leads. (a) Y junction where three armchair tubes join at 120°. (b) T junction where two armchair nanotubes join with a semiconducting zigzag nanotube. (c) Y junction where three armchair nanotubes join forming an angle of 72° between the upper arms. (d) T junction where two semiconducting zigzag nanotubes join with an armchair nanotube. Both Y junctions have heptagonal rings whereas the T junctions achieved their relaxed structure by the introduction of four octagons and two pentagons. After relaxation, the average bond length of the heptagons is 2.02% larger in (a) and 1.47% larger in (c) than the bond length of the hexagonal network. In the case of the T junctions the average bond length of the octagons is in (b) and (d) 1.35% larger, the bond lengths in the pentagons not shared with the octagons are nonetheless smaller than that of the hexagons by 1.07% in (b) and 1.31% in (d). These values are reasonable for having stable configurations. The defects pointed by the arrows are shown in more detail in the next figures.

Figure 2

(Color online) Projected DOS for the T junction, Fig. 1d, for the structure as relaxed using a Tersoff-Brenner potential with molecular dynamics (Ref. 36) (lighter color) and after relaxation with DFTB (Ref. 52) (darker line). Even if the different relaxation methods yield visibly different structures at the junction saddle zones, the DOS around the Fermi energy (with a distance-dependent hopping parameter) is nearly equal.

Figure 3

(Color online) DOS (projected on the junction) and conductance of the Y junction shown in Fig. 1a as a function of the incident electron energy. The inset in the upper panel shows the defect region pointed by the arrow in Fig. 1a with the atomic distribution of the LDOS at a localized state, whose conductance can be seen in the inset of the middle panel. The LDOS takes values from zero (white) to a its maximum value in dark-blue. The evolution of the atomic distribution of the LDOS at the junction have been followed up in an energy window around the Fermi level (Ref. 54). In the inset of the middle panel we see a blowup of $G_{12}^{\mathrm{el}}$ near the Fermi energy where resonant states are observed. The conductance is in units of the conductance quantum $2e^2∕h$. In the lower panel the total conductance $G_{12}^{\mathrm{tot}}$ for the upper arms of the junction when making a voltage probe out of the third lead is presented (dark line) together with the conductance of the perfect infinite CNT of chirality matching that of the source-drain tubes, in this case the (6,6) CNT (light line). In the inset here we plot the inelastic contribution to the conductance through the upper arms.

Figure 4

(Color online) The same properties as in Fig. 3 are plotted here for the T junction of Fig. 1b. In the insets the asymmetric line shapes corresponding to a Fano resonance are clearly observed.

Figure 5

(Color online) The same properties as in Fig. 3 are plotted here for the Y junction of Fig. 1c.

Figure 6

(Color online) The same properties as in Fig. 3 are plotted here for the T junction of Fig. 1d.

Figure 7

(Color online) Current vs gate voltage using one arm of the three-terminal junctions as gate electrode $\left({\mathrm{L}}_3\right)$. The switch on of the gate shows to be of interest for possible future applications of these junctions, and especially of the second of the Y-shaped ones. The labels $a$, $b$, $c$, and $d$ correspond to the notation given in Fig. 1 for the four considered junctions.

Figure 8

(Color online) Current $I_3$ vs bias voltage for the four junctions of Fig. 1. $I_3$ is the total current through lead ${\mathrm{L}}_3$—that is, $I_3=I_{31}+I_{32}$. The current is calculated for the experimental setup described in Eq. (19) as well as for a different situation given by Eq. (20) and plotted in the inset. As in the previous figure the labels $a$, $b$, $c$, and $d$ correspond to the notation given in Fig. 1 for the four junctions we consider.