Ab initio study of single-wall ${\mathrm{BC}}_2\mathrm{N}$ nanotubes

First-principles calculations based on a density functional theory were carried out to investigate electronic properties of ${\mathrm{BC}}_2\mathrm{N}$ nanotubes. It was found that the strain energy of the ${\mathrm{BC}}_2\mathrm{N}$ nanotube depends on the diameter but independent of the chirality of the tube. The electronic properties, however, are closely related to both the diameter and chirality of the tube. Generally, all ${\mathrm{BC}}_2\mathrm{N}$ nanotubes, except for a few with very small diameters, are direct gap semiconductors. Both the top valence band and the bottom conduction band are formed by carbon $p$ orbitals normal to the tube surface.

Figure 1

(Color online) The total energies of ${\mathrm{BC}}_2\mathrm{N}$ nanotubes as a function of the tube diameter. The horizontal dashed line indicates the energy of a ${\mathrm{BC}}_2\mathrm{N}$ sheet.

Figure 2

The calculated band structures (a) ZZ-1 (6,0), (b) ZZ-1 (9,0), (c) ZZ-1 (10,0), (d) ZZ-2 (0,3), (e) AC-1 (5,5), and (f) AC-2 (5,5) nanotubes.

Figure 3

The band gaps of various types of ${\mathrm{BC}}_2\mathrm{N}$ nanotubes as a function of the tube diameter. The number refers to the index $n$ for ZZ-1 $(n,0)$. The horizontal dashed line indicates the band gap of a ${\mathrm{BC}}_2\mathrm{N}$ sheet.