Zone-center instability of C(5,0) carbon nanotubes inside $\mathrm{Al}\mathrm{P}{\mathrm{O}}_4\text{−}5$ channels

The electronic structure of C(5,0) carbon nanotubes inside zeolite channels is analyzed. We confirm the occurrence of the metal-semiconductor transition which has been previously predicted in the case of isolated tubes. The interaction with the zeolite matrix does not prevent the spontaneous metal-semiconductor instability at room temperature, even though it reduces the magnitude of the band gap in the distorted stable phase. An empirical potential modeling, which allows the study of the tube and zeolite relaxation without the constraint of periodic boundary conditions, does not lead to the conclusion that some tubes could remain metallic.

Figure 1

Band structure of the (a) undeformed and (b) deformed tubes. The Fermi level is set to zero in both graphs and indicated with a discontinuous line. The labels for the symmetry representations of the relevant bands around the Fermi level are indicated; in (a) the numbers on the dispersion curves indicate their degeneracy. (a) $D_{5d}$ and (b) $C_{2h}$ point groups.

Figure 2

Sketch of the potential energy surface of the C(5,0) tube as a function of the axial deformation. (a) Isolated tubes, double well potential surface type, with a global minimum at the deformed tube structure. (b) Bundle of tubes, the tube-tube interaction induces a breaking of the $D_{5d}$ symmetry and only one minimum exist.

Figure 3

Band structure of a bundle of C(5,0) nanotubes with $4.0\mathrm{\AA }$ interwall distance. While the direct energy band gap at $\Gamma$ is $\approx 0.2\mathrm{eV}$, there is a tendency to close the gap at the $K$ point of the hexagonal Brillouin zone $({\mathrm{E}}_{\mathit{\text{gap}}}=0.08\mathrm{eV})$.

Figure 4

(Color online) Transversal cross section of the wave functions 40 and 41 at $\Gamma$ before $\left(E_{2u}\right)$ the deformation of the tube and opening of the gap. The ungerade character of the states is evident in the plot.

Figure 5

(Color online) (a) Unit cell of the $\mathrm{C}(5,0)+\mathrm{Al}\mathrm{P}{\mathrm{O}}_4\text{−}5$ complex seen along the [001] direction. (b) Lateral view of the unit cell showing the very good match between O rings and C(5,0) carbon zigzag chains.

Figure 6

Band structure around the Fermi level for the distorted tube inside the zeolite channel.

Figure 7

(Color online) (a) Side view of the undistorted AFI-C(5,0) complex. (b) Side view of the complex after distortion of both the AFI channels and C(5,0) CNT. (c) Top view of a distorted CNT inside the AFI channel with its distortion axis indicated. (d) The distortion axis changes after the tube is rotated and let to relax again.

Figure 8

Evolution of the total energy (top) and band-gap energy for a distorted tube as a function of its rotational angle around its own axis.

Figure 9

(Color online) Elastic energy stored in the zeolite frame per channel as a function of the total number of channels and tubes (see text).