Excitons in Boron Nitride Nanotubes

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

C.H. Park, C.D. Spataru, and Steve Louie

PRL 96, 126105 (2006)

URL: http://link.aps.org/abstract/PRL/v96/e126105

I took two main points from this paper.

First, the larger band gap in boron nitride nanotubes makes particle interactions even more important. The shift of the free particle band gap due to electron interactions is larger than in nanotubes, and the exciton binding energies are also larger. The authors do not present any scaling results as they only analyzed a single nanotube.

Second, the exciton is much more localized in boron nitride nanotubes than in carbon nanotubes. In a carbon nanotube, there is little variation in the magnitude of the exciton wave function around the tube circumference. In boron nitride, there is quite a lot of variation. The electron is localized around the hole, and the probability of finding it on the opposite side of the tube is very small. The amplitude is also strongly peaked on the boron sites.

In effect, the second result implies the excitons in boron nitride are qualitatively different than in carbon. They cannot be considered one-dimensional objects. The exciton envelope function in a carbon nanotube is a smooth localized function. That of a boron nitride nanotube must describe the variations in amplitdue between the two sublattices. The boron nitride exciton is a two-dimensional wave function that happens to live on a cylinder. It is not strongly influenced by the periodic boundary conditions. (At least not in the tube studied here. In a tube with a smaller radius, the amplitude might not decay to zero over half a circumference.)

An interesting question that has probably been answered: Are the excitons in a boron nitride nanotube much different from those of a boron nitride sheet? The sheet has 3-fold rotational symmetry, which the tube does not. However, the tightly-localized excitons in the tube might not "be able to tell the difference," so to speak. There are no excitons in graphene because it is a semi-metal with no band gap. The large gap of planar boron nitride should allow for excitons, and I would expect them to be quite similar to their nanotube analogs.