Monday, November 16, 2009

Graphene, part I

Graphene is one of the hottest materials out there right now in condensed matter physics, and I'm trying to figure out what tactic to take in making some blog postings about it.  One good place to start is the remarkably fast rise in the popularity of graphene.  Why did it catch on so quickly?  As far as I can tell, there are several reasons.
  1. Graphene has a comparatively simple electronic structure.  It's a single sheet of hexagonally arranged carbon atoms.  The well-defined geometry makes it extremely amenable to simple calculational techniques, and the basic single-particle band structure (where we ignore the fact that electrons repel each other) was calculated decades ago.
  2. That electronic structure is actually pretty interesting, for three reasons.  Remember that a spatially periodic arrangement of atoms "picks out" special values of the electron (crystal) momentum.  In some sense, electrons with just the right (effective) wavelength (corresponding to particular momenta) diffract off the lattice.  You can think of the hexagonal graphene lattice as a superposition of two identical sublattices off-set by one carbon-carbon bond length.  So, the first interesting feature is that there are two sets of momenta ("sets of points in reciprocal space") that are special - picked out by the lattice, inequivalent (since the two sublattices really are distinct) but otherwise identical (since it's semantics to say which sublattice is primary and which is secondary).  This is called "valley degeneracy", and while it crops up in other materials, the lattice symmetry of graphene ends up giving it added significance.  Second, when you count electrons and try filling up the allowed electronic states starting at the lowest energy, you find that there are exactly two highest energy filled spatial states, one at each of the two lowest-momentum inequivalent momentum points.  All lower energy states are filled; all higher energy states are empty.  That means that graphene is exactly at the border between being a metal (many many states forming the "Fermi surface" between filled and empty states) and a semiconductor (filled states and empty states separated by a "gap" of energies for which there are no allowed electronic states).  Third and most importantly, the energy of the allowed states near those Fermi points varies linearly with (crystal) momentum, much like the case of an ultrarelativistic classical particle, rather than quadratically as usual.  So, graphene is in some ways a playground for thinking about two-dimensional relativistic Fermi gases.
  3. The material is comparatively easy to get and make.  That means its accessible, while other high quality two-dimensional electron systems (e.g., at a GaAs/AlGaAs interface) require sophisticated crystal growth techniques.
  4. There is a whole literature of 2d electron physics in Si and GaAs/AlGaAs, which means there is a laundry list of techniques and experiments just waiting to be applied, in a system that theorists can actually calculate.
  5. Moreover, graphene band structure and materials issues are close to that of nanotubes, meaning that there's another whole community of people ready to apply what they've learned.
  6. Graphene may actually be useful for technologies!
Next time I post about this, I'll try to talk more about the special aspect of the valley degeneracy.

10 comments:

woot said...

Part of it is also a fad. It was like this for nanotubes too. It's not entirely clear to me why nearly all of condensed matter wants to work on something where the danger of being scooped is so severe, but apparently they do. It's also a little puzzling to me where some of the differentiation is when it comes to getting funding. Are all of these proposals really that different, I really can't imagine that they are.

Anonymous said...

Dear Doug, I could not resist leaving a message in your blog.

Firstly, you hit the target in many aspects on why graphene has attracted so much interest from the basic science point of view.

Moreover, from the applied point of view graphene is already showing its great potential and many big companies such as Samsung, Fujitsu, Intel, IBM, are investing heavily on the development of all sorts of electronic devices. SKKU and Samsung in South Korea, for instance, now produce graphene wafers routinely using simple CVD methods (hence, the issue of mass production has literally been solved).

Moreover, the funding for graphene research worldwide is hitting close to US $ 0.5 billion (in the USA, the Department of Defense is one of the major supporters).

Graphene is extremely stable structurally and another huge application that you will see soon is on impermeabilization of surfaces.

Also, graphene, unlike fullerenes, has been in the realm of the physicists in the last 4 years but chemists are now moving fast into the field and I hope other wonders will come up soon enough.

Doug, correct me if I am wrong but you were the chairman of the first graphene session of the APS March Meeting in Los Angeles in 2005. The Science paper by Nosovelov at al. had just been published a few months before in Science. I recall that in the room there were something like 20 people including Geim, Kim, de Heer, and Dresselhaus. Next year approximately 15% of all abstracts of the APS March Meeting in Portland will be on Graphene. I was lucky enough to be there too and witness the birth of a new research field. From my perspective, this is just the beginning.

Cheers, Antonio.

Alex Hamilton said...

I am very interested in the graphene business, but I wonder if over 90% of the work in this area isn't 'me-too' science. Linear dispersions etc have existed in carbon nanotubes for a long time. Similarly the physics of 2D systems has been extensively studied in GaAs systems. So where exactly is the _new_ physics?

Don Monroe said...

All good points. But it seems clear that the "ease of preparation" is solely responsible for the recent explosion of interest, no? Much of the rest (maybe not the "relativistic" dispersion relation) was well known when Millie Dresselhaus and others were looking at intercalated graphite 30 years ago.

It also seems that the ease of preparation cuts both ways for graphene, as it does for nanotubes. One-of-a-kind free-floating samples assembled using GSWT (graduate student with tweezers) may have a low barrier to entry, but they are not the basis of a technology.

Doug Natelson said...

woot - Yes, condensed matter tends to be faddish. There is a large pool of people, each with their particular tool or expertise (some specific electronic structure calculation or scattering technique or thermodynamic measurement or scanned probe), and when a new material system comes along that is sufficiently interesting, they pounce. The superconductivity community leaped on MgB2 pounded the whole area into submission in about a year. To some extent, the 2d electron and nanotube communities are doing the same thing to graphene. My personal attitude with graphene, as with nanotubes, has been to stay out unless I have a particular capability or experiment that I think is truly unique and can address some question that is important and otherwise being ignored.

Antonio - Possibly the best professional service I've done to the CM community was hunting down the abstracts from the Geim, Kim, DeHeer, and McEuen groups (all submitted to different sorting categories) and sticking them all in one session. That was fun.

Alex - I largely agree, in the sense that I am tired of papers on graphene where some effect is measured that either was predicted long before or is perfectly understood within a simple single-particle picture. Similarly, mobility or sub-threshold slope contests hold no charm for me. I think experimental probes of Klein tunneling are cute, as that's an effect that is not easy to access in any other system that I know about. The fractional quantum Hall papers from this past week are also interesting, since the FQHE really looks at electron-electron interactions, something largely ignored so far.

Don - I think you may be overstating the role of ease of entry into the field; there are lots of materials that are easy to get that haven't had the same excitement. It's the combo of ease of access and the comparative forgivingness of the system. Also, you're absolutely right that the scotch tape approach is very far from industrial applications. Still, between the SiC folks and the CVD-on-Cu approach, this seems more likely to be applicable than nanotubes.

Uncle Al said...

A single one-atom thick layer of graphene is visible! Graphene optical absorption is (pi)(alpha), 3.141593/137.0360 ~ 2.29%. It has a refractive index around 300,

http://math.ucr.edu/home/baez/week277.html
Science 320 1308 (2008)
http://onnes.ph.man.ac.uk/nano/Publications/Science_2008fsc.pdf
arXiv:0812.1116

MgB2, CrB2, TiB2 ZrB2 have 2-D graphenoid boron sheets spaced by M(+2). Cook 'em up with Me3SiCl to isolate the sheets? Ion-exchange with gemini surfactant to intercalcate and swell the sheets apart? Don't entrust a physicist or engineer with a stuff problem. They are skilled with things.

sylow said...

One thing is for sure. Columbia University leads the graphene fad. They have another paper in this week's Nature. Two weeks in a row. Not bad, huh?

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Graphene will lead to flying saucers and plates and tea cups all in a row. Tan tara ;o) I mean really, who do they think they are kidding. Just like the materials woven from spider's genes spliced into Goats producing a super fine fiber when woven from the goat's milk. Come on now. I mean really?

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Offcourse Graphene is one of the hottest materials in matter, if we see its atomic weight along with its mass volume, then anyone can easily analysis its electronic structure.