Excitons and Many-Electron Effects in the Optical Response of Single-Walled Boron Nitride Nanotubes

We report first-principles calculations of the effects of quasiparticle self-energy and electron-hole interaction on the optical properties of single-walled boron nitride nanotubes. Excitonic effects are shown to be even more important in BN nanotubes than in carbon nanotubes. Electron-hole interactions give rise to complexes of bright (and dark) excitons, which qualitatively alter the optical response. Excitons with a binding energy larger than 2 eV are found in the $(8,0)$ BN nanotubes. Moreover, unlike the carbon nanotubes, theory predicts that these exciton states are comprised of coherent supposition of transitions from several different subband pairs, giving rise to novel behaviors.

Figure 1

Difference between the $GW$ quasiparticle energy and the LDA Kohn-Sham eigenvalue (a) and quasiparticle band structure (b) for the $(8,0)$ SWBNNT. Empty circles in (a) and the dashed line in (b) show the nearly free-electron tubule states.

Figure 2

Absorption spectra of the $(8,0)$ SWBNNTs. The imaginary part of the polarizability per tube ${\alpha }_2(\omega )$ is given in unit of ${\mathrm{nm}}^2$. (See text.) The spectra are broadened with a Gaussian of 0.0125 eV.

Figure 3

(a)–(c) Wave function of the lowest-energy bright exciton of the $(8,0)$ SWBNNT. (a) Isosurface plot of electron probability distribution $|\Phi ({\mathbf{r}}_e,{\mathbf{r}}_h){|}^2$ with the hole fixed at the position indicated by black star. (b) $|\Phi ({\mathbf{r}}_e,{\mathbf{r}}_h){|}^2$ averaged over tube cross section. Hole position is set at zero. (c) $|\Phi ({\mathbf{r}}_e,{\mathbf{r}}_h){|}^2$ evaluated on a cross-sectional plane of the tube. (d)–(f) Wave function of the lowest-energy bright exciton of the $(8,0)$ SWCNT. Plotted quantities are similar to those in (a)–(c).

Figure 4

Wave functions of excitons of the $(8,0)$ SWBNNT. Plotted quantities are similar to those in Fig. 3b.