Length-dependent transport properties of $(12,0)∕(n,m)∕(12,0)$ single-wall carbon nanotube heterostructures

We study the length-dependent transport behaviors of $(12,0)∕(n,m)∕(12,0)$ heterostructures using a $\pi$-orbital tight-binding model and a Green’s function technique. When $(n,m)$ is a semiconducting tube, or a (6,6) tube with sixfold rotational symmetry ${\mathrm{C}}_6$ on the interfaces, conductance $G$ decreases exponentially with the length $L$ of the $(n,m)$ tube. However, we find an anomalous increase of $G$ with $L$ in the $(12,0)∕(9,0)∕(12,0)$ heterostructure. We explain this anomalous phenomenon and reproduce the transport behaviors of the heterostructure very well by introducing an exponentially dropped potential (EDP) around the interfaces. This model helps us to understand the physics of carbon nanotubes with finite lengths.

Figure 1

Four different types of sandwichlike single-walled carbon nanotube heterostructures: (a) $(12,0)∕(11,0)∕(12,0)$, (b) $(12,0)∕(8,4)∕(12,0)$, (c) $(12,0)∕(6,6)∕(12,0)$, and (d) $(12,0)∕(9,0)∕(12,0)$. $L$ denotes the spacing of the two most inner atoms of the two heptagons.

Figure 2

(Color online.) Length-dependent conductance at Fermi level of four different types of heterostructures: (a) $(12,0)∕(11,0)∕(12,0)$, (b) $(12,0)∕(8,4)∕(12,0)$, (c) $(12,0)∕(6,6)∕(12,0)$, and (d) $(12,0)∕(9,0)∕(12,0)$. The insets are semilog plots. Solid lines are fitted curves. Dots are results of the tight-binding calculation.

Figure 3

(Color online.) Conductance spectra for infinite nanotube junctions: (a) $(12,0)∕(6,6)$, (b) $(12,0)∕(9,0)$.

Figure 4

(Color online.) Conductance spectra for $(12,0)∕(9,0)∕(12,0)$ heterostructures in Fig. 1 with different $L$. From bottom to top: (1) $L=1.8\mathrm{\AA }$, (2) $L=10.2\mathrm{\AA }(+3)$, (3) $L=18.7\mathrm{\AA }(+6)$, (4) $L=23.0\mathrm{\AA }(+9)$. “$+3$,” “$+6$,” and “$+9$” are due to “$G+3G_0$,” “$G+6G_0$,” and “$G+9G_0$,” respectively.

Figure 5

(Color online.) Peak spacing (PS) vs $L$. Solid circles are from TB calculation and they correspond to 1, 2, 3, 4, and 5 unit cells of (9,0) tube, respectively. Solid line is the fitted curve according to Eq. (10). The inset is semilog plot.

Figure 6

(Color online.) $(12,0)∕(9,0)∕(12,0)$ heterostructure $(L=23.0\mathrm{\AA })$ and schematic plot of $V\left(x\right)(V_0=0)$ described by Eq. (8).