Electronic structure of boron-doped carbon nanotubes

We study boron-doped single-walled carbon nanotubes by using first-principles methods based on the density functional theory. The total energy, band structure, and density of states are calculated. From the formation energy of boron-doped nanotubes with different diameters, it is found that a narrower tube needs a smaller energy cost to substitute a carbon atom with a boron atom. By using the result of different doping rates in the (10,0) tube, we extrapolate the result to low boron density limit and find that the ionization energy of the acceptor impurity level should be approximately 0.2 eV. Furthermore, we discuss the doping rate dependence of the density of states at the Fermi level, which is important to realize superconductivity.

Figure 1

(Color online) Optimized structure of a boron-doped (10,0) carbon nanotube. There are 39 carbon atoms and 1 boron atom in the unit cell $\left({\text{BC}}_{39}\right)$. The doped boron atom moves outward via geometry optimization as illustrated by the arrow.

Figure 2

$\Delta E$ defined in Eq. (1) as a function of nanotube diameter. $\left(m,0\right)$ zigzag tubes of $m=4–12$ (filled circles) and $\left(m,m\right)$ armchair tubes of $m=4$, 5, and 6 (open circles) are plotted.

Figure 3

Band structures and DOSs of pristine and B-doped (10,0) SWCNT: (a) ${\text{C}}_{40}$, (b) ${\text{BC}}_{39}$, (c) ${\text{BC}}_{79}$, (d) ${\text{BC}}_{119}$, and (e) ${\text{B}}_2{\text{C}}_{78}$.

Figure 4

Gap of a B-doped (10,0) tube as a function of boron-boron distance $L$. The data are fitted by Eq. (2).

Figure 5

$D\left({ϵ}_F\right)$ of a B-doped (10,0) tube and B-doped diamond. For comparison, we also plot the density of states of a pristine (10,0) tube regarding the boron concentration as the hole density in the rigid-band picture.