Tag Archives: Graphene


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_xSe 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.

What Happens in 2D Stays in 2D.

There was a recent paper published in Nature Nanotechnology demonstrating that single-layer NbSe_2 exhibits a charge density wave transition at 145K and superconductivity at 2K. Bulk NbSe_2 has a CDW transition at ~34K and a superconducting transition at ~7.5K. The authors speculate (plausibly) that the enhanced CDW transition temperature occurs because of an increase in electron-phonon coupling due to the reduction in screening. An important detail is that the authors used a sapphire substrate for the experiments.

This paper is among a general trend of papers that examine the physics of solids in the 2D limit in single-layer form or at the interface between two solids. This frontier was opened up by the discovery of graphene and also by the discovery of superconductivity and ferromagnetism in the 2D electron gas at the LAO/STO interface. The nature of these transitions at the LAO/STO interface is a prominent area of research in condensed matter physics. Part of the reason for this interest stems from researchers having been ingrained with the Mermin-Wagner theorem. I have written before about the limitations of such theorems.

Nevertheless, it has now been found that the transition temperatures of materials can be significantly enhanced in single layer form. Besides the NbSe_2 case, it was found that the CDW transition temperature in single-layer TiSe_2 was also enhanced by about 40K in monolayer form. Probably most spectacularly, it was reported that single-layer FeSe on an STO substrate exhibited superconductivity at temperatures higher than 100K  (bulk FeSe only exhibits superconductivity at 8K). It should be mentioned that in bulk form the aforementioned materials are all quasi-2D and layered.

The phase transitions in these compounds obviously raise some fundamental questions about the nature of solids in 2D. One would expect, naively, for the transition temperature to be suppressed in reduced dimensions due to enhanced fluctuations. Obviously, this is not experimentally observed, and there must therefore be a boost from another parameter, such as the electron-phonon coupling in the NbSe_2 case, that must be taken into account.

I find this trend towards studying 2D compounds a particularly interesting avenue in the current condensed matter physics climate for a few reasons: (1) whether or not these phase transitions make sense within the Kosterlitz-Thouless paradigm (which works well to explain transitions in 2D superfluid and superconducting films) still needs to be investigated, (2) the need for adequate probes to study interfacial and monolayer compounds will necessarily lead to new experimental techniques and (3) qualitatively different phenomena can occur in the 2D limit that do not necessarily occur in their 3D counterparts (the quantum hall effect being a prime example).

Sometimes trends in condensed matter physics can lead to intellectual atrophy — I think that this one may lead to some fundamental and major discoveries in the years to come on the theoretical, experimental and perhaps even on the technological fronts.

Update: The day after I wrote this post, I also came upon an article demonstrating evidence for a ferroelectric phase transition in thin Strontium Titanate (STO), a material known to exhibit no ferroelectric phase transition in bulk form at all.

Do “Theorems” in Condensed Matter Physics Limit the Imagination?

There are many so-called “theorems” in physics. The most famously quoted in the field of condensed matter are the ones associated with the names of Goldstone, Mermin-Wagner, and McMillan.

If you aren’t familiar with these often (mis)quoted theorems, then let me (mis)quote them for you:

1) Goldstone: For each continuous symmetry a phase of matter breaks, there is an associated collective excitation that is gapless for long wavelengths, usually referred to as a Nambu-Goldstone mode.

2) Mermin-Wagner: Continuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions d ≤ 2. (From Wikipedia)

3) McMillan (PDF link!): Electron-phonon induced superconductivity cannot have a higher Tc than approximately 40K.

All these three theorems in condensed matter physics have been violated to a certain extent. My gut feeling, though, is that these theorems can have the adverse consequence of limiting one’s imagination. As an experimental physicist, I can see the value in such theorems, but I don’t think that it is constructive to believe them outright. The number of times that nature has proven that she is much more creative and elusive than our human minds should tell us that we should use these theorems as guidance but to always be wary of such ideas.

For instance, had one believed the Mermin-Wagner theorem outright, would someone have thought the existence of graphene possible? In a solid, which breaks translational symmetry in three directions and rotational symmetry in three directions, why are there only three acoustic phonons? McMillan’s formula still holds true for electron-phonon coupled superconductors (marginal case being MgB2 which has a Tc~40K), though a startling discovery recently may even shatter this claim. However, placed in its historical context (it was stated before the discovery of high-temperature superconductors), one wonders whether McMillan’s formula disheartened some experimentalists from pursuing the goal of a higher transition temperature superconductor.

My message: One may use the theorems as guidance, but they are really there to be broken.