Honeycomb 2-dimensional graphene carbon lattice (l); and frontal and side representations of Dirac cones touching in momentum space.
Graphene is a good thermal conductor, better than silicon. That property means that a device — say, a transistor — made out of graphene could vent its own heat. Though the material itself dissipates heat, “graphene” as a research topic has been getting hotter and hotter.
In a recent assessment of frequency of search terms input on the Nature Magazine web site, “graphene” ranked first. Second and third places went respectively to “HIV” and to “cancer.” The latter two terms, encompassing vast research enterprises, are household words. In contrast, few folks who are not physical scientists or engineers know for sure what graphene is, though they might make a homophonic-based guess that graphene has something to do with graphite—the substance whence pencils are made.
Graphene is, in fact, a sheet of graphite. Graphene consists of a single layer of carbon atoms arranged in a hexagonal or honeycomb lattice wherein electron movement is de facto confined to two dimensions.
Why is graphene such a hot scientific subject? Because, said Sankar Das Sarma of the University of Maryland who led the weeklong graphene workshop that was embedded in the KITP “Low Dimensional Electron Systems” program, “With graphene comes the prospect of an enabling technology that could transform civilization.”
How transform? One possible answer is that graphene may provide the material means for circumventing the projected silicon roadblock, whereby the exponential march of technological innovation based on the integrated circuit slows or even stalls. The pace of that innovation — doubling digital data density at roughly 1.5-to-3-year intervals (i.e., Moore’s law) has governed the development of business models in industries based on the integrated circuit (which comprise much of what we mean by “high tech”).
Though agnostic about graphene’s prospects for acting as a silicon substitute at the critical juncture where Moore’s law begins to fail, Das Sarma points out that this new material exhibits properties enough different from silicon that graphene may enable applications so different and so remarkable that they can as yet not be envisioned.
As tantalizing to condensed matter theorists as the prospect of pioneering the next transformative technology is the fact that a real material exists wherein electrons moving from carbon atom to carbon atom in a two-dimensional honeycomb lattice obey the same equation that neutrinos follow or, in other words, the Dirac equation for massless particles in free space. (Actually, neutrinos have a very small mass, but so small that they can be treated as massless.)
Sankar Das Sarma
“It is mind-boggling,” said Das Sarma. “Here is a two-dimensional electron system for which the basic equation comes from relativistic quantum mechanics.”
When an object moves with velocity (v), it has kinetic energy. Electrons in an ordinary system obey Newton’s equation whereby energy increases quadratically in relation to velocity (E ~ v2). But in graphene, the energy of electrons increases linearly with velocity (E ~ v), as if the electrons were relativistic, massless particles that obey Dirac’s equation. The first equation is Newton; the second, Dirac; and the first is non-relativistic; the second, relativistic.
“So much of the ‘fundamental’ interest in graphene,” said Das Sarma, “is coming from the fact that there is no material like it.”
Physicists knew in the 1940s the unusual properties of a single sheet of carbon atoms, but back then, said Das Sarma, “Nobody thought you could actually have a single sheet of carbon atoms.” Scientists thought that graphene was a hypothetical material.
In 2004, Russian scientists, working at the University of Manchester in Great Britain, discovered how to make graphene by using Scotch tape to peel off a graphene sheet from graphite. The following year, they showed that the quasiparticles in graphene were massless Dirac fermions — i.e., electrons behaving like neutrinos. They showed that the system exhibited a quantum Hall effect, and that the effect pertained at room temperature because it is so stable.
“Every graphene laboratory,” quipped Das Sarma, “has a big supply of Scotch tape. Not all the flakes are a single layer of carbon atoms, but some are, and those are graphene. In these days of high-tech fabrication,” he said, “it is amazing that pencil flakes and Scotch tape should provide the gateway to a new material and likely a transformative technology.”
Another distinctive property of graphene is its zero-width band gap. Das Sarma said, “That’s a strange system because it can be classified as a metal or a semiconductor. We can dope the material and then add a metal gate and electric fields so electrons go in or out. Because the electrons can go in or out, applications based on such a system can use either electrons or holes,” said Das Sarma. [“Holes” are electron absences with, therefore, positive charge.] “And,” added Das Sarma, “an application can change from using electrons to using holes because the band-gap is zero. When a positive voltage is applied, holes flow because electrons are repelled; if a negative voltage is applied, electrons flow. So current can be manipulated, and that operation affords the prospect for a new kind of electronics.”
As the program description for the KITP Rapid Response workshop (“Electronic Properties of Graphene,” held at the outset of 2007) averred, “Because of its high electronic mobility, structural flexibility, and capability of being tuned from p-type to n-type doping by the application of a gate voltage, graphene is considered a potential breakthrough in terms of carbon-based nano-electronics.”
Das Sarma, who led the effort to calculate the vacuum polarization for graphene (i.e., its screening properties), structured the 2009 KITP graphene workshop around the reporting of experimental results. “Five experimentalists gave two-hour talks in the morning; all of them talked about new results. We theorists learned so many new things.” He said that the flurry of results were harbingers of breakthroughs to come.
“Graphene is big,” said Das Sarma, “and it is going to get bigger.”