Effect of localized oxygen functionalization on the conductance of metallic carbon nanotubes

A comprehensive study of the effect of covalent oxygen attachment on the transmission and conductance of armchair and metallic zigzag carbon nanotubes (CNTs) is presented. In both armchair and zigzag CNTs covalent oxygen attachment favors an ether-type bond in which the C-C bond breaks. Oxygen atoms attached on the CNT surface within the same carbon ring on parallel bonds are energetically more stable than well-separated attachments. In an armchair CNT, oxygen attachment favors the C-C bonds orthogonal to the CNT axis. Cooperative addition propagates axially along parallel orthogonal bonds. In a zigzag CNT, oxygen attachment prefers the slanted bond, and cooperative addition propagates spirally along parallel slanted bonds. Closely spaced oxygen attachment on the armchair and zigzag CNT surfaces causes a dip in transmission symmetrically away from the Fermi level at the turn-on of the first excited modes. For both armchair and zigzag CNTs, as more oxygen atoms are placed in close proximity, their levels interact and split and move closer to the Fermi level which results in broader dips in transmission closer to the Fermi level. The transmission of armchair CNTs near the charge-neutral Fermi level is relatively insensitive to a group of localized oxygen atoms compared to that of metallic zigzag CNTs. A clustered group of oxygen atoms covalently attached to a single-walled metallic zigzag CNT can result in a 1 order of magnitude drop in transmission that is asymmetric with respect to the Fermi energy resulting in a qualitative resemblance to conductance versus gate voltage curves observed experimentally. The covalent attachment of a single oxygen atom in any configuration, on either, an armchair, or zigzag metallic CNT does not give rise to a large change in conductance. Calculations use density-functional theory combined with nonequilibrium Green’s functions.

Figure 1

(Color online) Section of an armchair CNT illustrating the two types of bonds, orthogonal and slanted. Arabic numerals label the bonds and Roman numerals label the rings. The red atom at bond 1 is the oxygen atom. “Orthogonal” denotes the bonds that are orthogonal to the axial direction such as bonds 1, 4, 6, and 8. “Slanted” denotes the other type of bond such as 2, 3, 5, 7, and 9.

Figure 2

(Color online) (7,7) CNT with a cooperative ether configuration of oxygen atoms in red on the orthogonal bonds repeated in the axial direction. (a) Relaxed structure with three cooperative ethers along the axial direction. (b) Transmission plots labeled according to the number of oxygen atoms. The transmission of the pristine CNT (dashed) is shown for comparison.

Figure 3

(Color online) (7,7) CNT with a noncooperative ether configuration of oxygen atoms in red on the orthogonal bonds repeated in the circumferential direction. (a) Relaxed structure with three noncooperative oxygen atoms. (b) Transmission plots labeled according to the number of oxygen atoms (plot for two oxygen atoms lies between 1 and 3). The dashed line is the transmission of the pristine CNT shown for comparison. Inset: transmission with one oxygen atom.

Figure 4

(Color online) $E\text{−}k$ plot of (7,7) CNT with oxygen atoms on the orthogonal bonds. (a) Five cooperative oxygen atoms with configuration and supercell length as shown in Fig. 2 and (b) seven well-separated oxygen atoms with configuration and supercell length as shown in Fig. 3. The black lines are the CNT bands resulting from its constituent carbon atoms. The red circled, horizontal lines indicate localized states resulting from the oxygen atoms.

Figure 5

(Color online) (7,7) CNT with cooperative epoxide oxygen atoms on the slanted bonds repeated in the spiral direction. (a) Relaxed structure with three cooperative epoxide oxygen atoms. (b) Transmission plots labeled according to the number of oxygen atoms.

Figure 6

(Color online) Section of a zigzag CNT illustrating the two types of bonds, axial and slanted. Arabic numerals label the bonds and Roman numerals label the rings. The red atom at bond 1 is the oxygen atom. “Axial” denotes the bonds that are parallel to the axial direction such as bonds 2 and 5. Slanted denotes the other type of bond such as 4 and 7.

Figure 7

(Color online) (12,0) CNT with cooperative ether configuration oxygen atoms on the slanted bonds repeated in the spiral direction. (a) Relaxed structure with three cooperative oxygen atoms. (b) Transmission plots labeled according to the number of oxygen atoms.

Figure 8

(Color online) (12,0) CNT with a noncooperative ether configuration of oxygen atoms on the slanted bonds repeated in the circumferential direction. (a) Relaxed structure with three noncooperative oxygen atoms. (b) Transmission plots labeled according to the number of oxygen atoms.

Figure 9

(Color online) (12,0) CNT with cooperative epoxide oxygen atoms on the axial bonds repeated in the circumferential direction. (a) Relaxed structure with three cooperative epoxide oxygen atoms. (b) Transmission plots labeled according to the number of oxygen atoms.

Figure 10

(Color online) (7,7) CNT with 12 oxygen atoms (red) attached in ether configuration on the orthogonal bonds. (a) Relaxed structure with 12 cooperative oxygen atoms. (b) Relaxed structure with 12 well-separated oxygen atoms. (c) Transmission plot for cooperative (red) and well-separated (blue) oxygen atoms.

Figure 11

(Color online) (12,0) CNT with 16 oxygen atoms on the slanted bonds on the upper surface. (a) Structure of parallel spiral lines each containing three O atoms with one row gap between them (cooperative alternating). (b) Structure of parallel spiral lines each containing three O atoms with no gap or 16 clustered O atoms (cooperative adjacent). (c) Transmission plot for cooperative clustered (red online), cooperative one row gap (blue online) and well-separated (labeled as “sparse”) (green online) oxygen distributions. (d) Conductance versus $E_f$ of the cooperative clustered (red online), cooperative one row gap (blue online) and well-separated (labeled as sparse) (green online) oxygen distributions.