# Tag Archives: Carbon Nanotubes

## Timing

Rather than being linear, the historical progression of topics in physics sometimes takes a tortuous route. There are two Annual Reviews of Condensed Matter Physics articles, one by P. Nozieres and one by M. Dresselhaus, that describe how widespread interest on certain subjects in the study of condensed matter were affected by timing.

In the article by Dresselhaus, she notes that HP Boehm and co-workers had actually isolated monolayer graphene back in 1962 (pdf!, and in German). On the theoretical front, P. Nozieres says in his article:

But neither I nor any of these famous people ever suspected what was hiding behind that linear dispersion. Fifty years later, graphene became a frontier of physics with far-reaching quantum effects.

Dresselhaus also mentions that carbon nanotubes were observed in 1952 in Russia followed by another reported discovery in the 1970s by M. Endo. These reports occurred well before its rediscovery in 1991 by Iijima that sparked a wealth of studies. The controversy over the discovery of nanotubes actually seems to date back even further, perhaps even to 1889 (pdf)!

In the field of topological insulators, again there seems to have been an oversight from the greater condensed matter physics community. As early as 1985, in the Soviet journal JETP, B.A. Volhov and O.A. Pankratov discussed the possibility of Dirac electrons at the surface between a normal band-gap semiconductor and an “inverted” band-gap semiconductor (pdf). Startlingly, the authors suggest CdHgTe and PbSnSe as materials in which to investigate the possibility. A HgTe/(Hg,Cd)Te quantum well hosted the first definitive observation of the quantum spin hall effect, while the Pb$_{1-x}$Sn$_x$Se system was later found to be a topological crystalline insulator.

One can probably find many more examples of historical inattention if one were to do a thorough study. One also wonders what other kinds of gems are hidden within the vastness of the scientific literature. P. Nozieres notes that perhaps the timing of these discoveries has something to do with why these initial discoveries went relatively unnoticed:

When a problem is not ripe you simply do not see it.

I don’t know how one quantifies “ripeness”, but he seems to be suggesting that the perceived importance of scientific works are correlated in some way to the scientific zeitgeist. In this vein, it is amusing to think about what would have happened had one discovered, say, topological insulators in Newton’s time. In all likelihood, no one would have paid the slightest attention.

## Plasmons of a Luttinger Liquid

There’s a quite remarkable experiment in a paper by the Wang group at Berkeley that recently came out in Nature Photonics demonstrating the existence of peculiar plasmons in carbon nanotubes. These are significant because this may constitute the first observations of plasmons in a Luttinger liquid. To observe these plasmons, the group used scattering-scanning near-field optical microscopy (s-SNOM).

The plasmons are novel in that they appear to have a quantized propagation velocity that depends only on the number of conducting channels. Also, the ratios for the propagation velocities appear to be in the form $1:\sqrt{2}:\sqrt{3}:\sqrt{4}$ for one, two, three and four nanotubes respectively. (Each nanotube has one conducting channel).

The plasmons are extremely well-confined spatially ($\lambda_p/\lambda \sim 1/100$, where $\lambda_p$ and $\lambda$ are the plasmon wavelength and the wavelength of free-space light respectively) and also have a quality factor of $\sim$20. This means that there may be important applications in store for these kinds of plasmons as well, though I find the result from a more fundamental perspective quite intriguing.