Conductance spectra of metallic carbon nanotube heterojunctions

A two-probe carbon nanotube (CNT) device is usually in the metal-CNT-metal configuration, whose conductance sensitively depends on details of the metal-CNT interfaces. When the metal leads are CNT themselves, namely, for single-wall CNT double intramolecular junctions in the form of $(n_1,m_1)∕(n_0,m_0)∕(n_1,m_1)$, due to rotational symmetry of the $(n_0,m_0)$ section and quantum inference established between the two $(n_1,m_1)∕(n_0,m_0)$ interfaces, rather universal behavior of conductance spectra is found with respect to the relative rotational angle $\theta$ between the two $(n_1,m_1)$ leads. In particular, we theoretically prove that the conductance spectra have either periodic dependences or no dependence at all on the angle $\theta$. We further prove that when there is $\theta$ dependence, at most three different conductance spectra are possible for all allowed $\theta$. Numerical results confirm the analytical prediction.

Figure 1

(Color online) (a) Geometries of $(6,6)∕{(12,0)}_6∕{(6,6)}^{\theta }$ for $\theta =0°$ and 30°. $\theta$ is the dihedral angle, i.e., the rotational angle of the left part of the QD relative to the right part. The subscript 6 means there are six units of (12,0) tube between the two interfaces. $x$ is the axis of the central tube (12,0). Side views are given at the right side. (b) Geometries of $(12,0)∕{(6,6)}_6∕{(12,0)}^{\theta }$ for $\theta =0°$ and 60°. $x$ is the axis of the central tube (6,6). Side views are given at the right side.

Figure 2

(Color online) (a) Conductance spectra of $(6,6)∕{(12,0)}_6∕{(6,6)}^{\theta }$ with $\theta =0°,30°,\dots ,330°$. Only two different curves of $G\left(E\right)$ are possible for all the allowed $\theta$, and $G$ changes periodically between the two curves with the period of $3\times 30°$. (b) Conductance spectra of $(12,0)∕{(6,6)}_6∕{(12,0)}^{\theta }$ with $\theta =0°,60°,\dots ,300°$. Only one curve of $G\left(E\right)$ for all the allowed $\theta$ for this device. The inset is the conductance spectra of $(12,0)∕(9,3)∕{(12,0)}^{\theta }$ with $\theta =0°,120°,240°$, respectively. For this system, there are three different $G\left(E\right)$ curves for all the allowed $\theta$.

Figure 3

(a) A segment of CNT with two point defects $A$ and $B$. $x$ is the axis of the tube. (b) The unwrapped plane of the cylindrical surface of (a). Points $B_0\left(B\right),B_1,\dots ,B_l$ are rotationally symmetrical points on the tube surface. ${\vec{a}}_1$ and ${\vec{a}}_2$ are lattice vectors of the graphene. ${\vec{C}}_h$ and $\vec{T}$ are the chiral vector and translational vector, respectively.