Conductance of a conjugated molecule with carbon nanotube contacts

The conductance of an experimentally measured metallic carbon nanotube (CNT)-molecule-CNT structure is calculated. The features in the predicted transmission correspond directly to the features of the isolated molecular orbitals and surface states of the cut ends of the CNTs. The highest occupied molecular orbital (HOMO) provides a weakly coupled conductive channel with transmission features that are qualitatively insensitive to the chemical end groups of the cut CNTs, the cut angle, the CNT chirality, and the number of molecular bridges. Quantitatively, however, these factors can modify the resonance width by an order of magnitude giving rise to corresponding changes in the resistance. Furthermore, the cut ends of a zigzag CNT can have surface states which hybridize with the molecular HOMO state giving a large transmission peak at the Fermi level. To understand the molecular energy-level alignment with the CNT Fermi level, a quantum chemical calculation of the ionization potential and electron affinity and a density-functional theory calculation of the CNT image potential are performed. A twist on molecular conformation-change switching is also suggested.

Figure 1

(Color online) (a) Relaxed CNT-molecule-CNT structure with armchair (7,7) CNT contacts. (b) Close-up of CNT-amide bond relaxed configuration. (c) Calculated transmission of the armchair CNT-molecule-CNT structure.

Figure 2

(a) Structure used for the calculation of the image potential. The molecule is removed and the connecting C atoms of the CNTs are terminated with H. A positive point charge is placed at a point corresponding to the center of the molecule. The open boundaries at the left and right CNT ends are included via self-energies, and the charge is calculated with the recursive Green’s function algorithm. (b) Potential profiles $\Phi$ (solid) and ${\Phi }^0$ (dashed) plotted along an axial line that lies on top of the CNT contacts and passes through the center of the point charge. The image potential at $x=0$ is used to renormalize the HOMO energy level. The small potential steps at $\pm 10\text{nm}$ are the result of the boundary conditions described in the text.

Figure 3

(Color online) (a) Three-dimensional contour plots of the covariant spectral function corresponding to the resonant peaks marked in Fig. 1. (b) Corresponding molecular orbitals for the relaxed isolated molecule in the planar conformation. Amide groups are included at the left and right ends of each molecule.

Figure 4

(Color online) (a) Relaxed CNT-molecule-CNT structure with zigzag (12,0) CNT contacts. (b) Close-up of CNT-amide bond configuration. (c) Calculated transmission of the zigzag CNT-molecule-CNT structure (solid) and the armchair CNT-molecule-CNT structure (dashed).

Figure 5

(Color online) (a) Calculated transmission close to the Fermi energy where the solid line represents the zigzag system and the dashed line represents the armchair system. (b) The spectral functions corresponding to the resonant transmission peaks marked in (a) for the zigzag CNT-molecule-CNT structure. Inset shows peaks clustered above and below $E_F=0\text{eV}$

Figure 6

(Color online) (a) Relaxed armchair CNT-molecule-CNT structure with two planar molecules attached. (b) Calculated transmission of CNT-molecule-CNT system shown in (a).

Figure 7

(Color online) (a) Top and side views of a relaxed CNT-molecule-CNT structure with the CNT side walls passivated with carboxyl group molecules. Bolder atoms and bonds in top view represent the cut edge of the CNTs. (b) Top and side views of a relaxed CNT-molecule-CNT structure with the CNT side walls passivated with carboxyl/hydrogen molecules. Bolder atoms and bonds in top view represent the cut edge of the CNTs. (c) Calculated transmission of CNT-molecule-CNT systems shown in (a) (solid) and (b) (dashed).

Figure 8

(Color online) (a) Top and side views of a relaxed CNT-molecule-CNT structure with the CNT side walls passivated with carboxyl group molecules and the molecule attached on top. Bolder atoms and bonds in top view represent the cut edge of CNTs. (b) Calculated transmission of CNT-molecule-CNT systems shown in (a).

Figure 9

(Color online) (a) Relaxed CNT-molecule-CNT structure with a perpendicular ethoxybenzene cross-arm conformation molecule attached. (b) Calculated transmission comparison where the solid line is for the system shown in (a) and the dashed line is for the planar ethoxybenzene cross-arm conformation shown in Fig. 1a. (c) Molecular HOMO-1 and HOMO orbitals for the relaxed isolated molecule in the perpendicular conformation with amide groups attached.

Figure 10

$5\text{M}\Omega$ equal-resistance contour in the $\Gamma -\left(E_F-E_{HOMO}\right)$ plane resulting from a Lorentzian transmission spectrum. (Inset) Position of the various energy levels used in the calculation.