Inevitably, diamond turns into graphite

August 2008: Wonder material from the pencil

A truck without petrol won't make it over the mountain. Similarly, a particle is stuck in a valley between two potential barriers. However, quantum mechanics, even in its normal, non-relativistic form, offers a loophole. A second version of Heisenberg's principle of indeterminacy says that it is impossible to know exactly both the location and the momentum of an object. The latter is practically zero for a particle hanging in an energy valley and is therefore known very precisely. As a result, there is a high level of uncertainty about the location. There is a certain probability that the particle can also be located behind the barrier: it has crossed it as if by magic. Physicists call this the tunnel effect.

In the non-relativistic case, the tunnel probability is quite low and decreases with increasing height and width of the barrier. In quantum electrodynamics, however, according to Klein, the situation is completely different. According to his theoretical considerations, relativistic particles should tunnel through very high, extensive obstacles with a probability of 100 percent. At the edge they simply mate with their antiparticle twin, for whom the world is, as it were, upside down, so that the mountain appears to him as a valley. After the passage, the ad hoc companion vanishes again into nothingness, from which it emerged briefly with borrowed energy, and the electron continues its journey as if nothing had happened. Even many physicists seem suspicious of this kind of ghost.

So the thing calls for experimental verification. For a long time, however, it was unclear what a test for the little paradox might look like or whether it might even be impossible in principle. The massless Dirac quasiparticles in graphs are just what you need. They turn the little paradox into a routine effect with easily observable consequences. You can artificially create potential barriers of different heights and widths in the graph and then measure the electrical conductivity. With a tunnel probability of 100 percent, it should not be reduced by the obstacles. Corresponding investigations are currently underway in various laboratories. Graphs can also be used to demonstrate other unusual consequences of quantum electrodynamics.

Ultra-fast transistors

But what about technical applications? It is still too early to give a definitive answer. What seems clear, however, is that any possible use for rolled graphene nanotubes is also open to the flat shape. However, it must be possible to produce the material on an industrial scale. Many research groups are working to develop improved manufacturing methods.

As dust, graphene can already be produced in industrial quantities. But it is still very difficult to obtain extensive leaves from the material, which is why it is probably the most expensive material of all. A micromechanically generated graphene mini-crystal that is thinner than a hair currently costs over a thousand dollars. Groups in Europe and at several US institutions including the Georgia Institute of Technology in Atlanta, the University of California at Berkeley, and Northwestern University in Evanston, Illinois have deposited graphene films on silicon carbide disks.

Integrated circuits that can be cut out of a single graphene plate would even be conceivable

In the meantime, engineers are also exploring the unique physical and electronic properties that make the material so technically interesting. With its high surface-to-volume ratio, it should be suitable for hard composite materials, for example. As an extremely thin material, it could also result in more efficient field emitters: devices that emit electrons from needle-shaped tips in the presence of strong electrical fields.

Since the properties of graphene can be precisely regulated with electric fields, there are good prospects of using the material to build ultra-sensitive chemical detectors as well as better superconducting and spin-valve transistors. Furthermore, thin films of overlapping pieces of graphene could provide transparent, electrically conductive coatings for liquid crystal displays and solar cells. The list is by no means exhaustive, and some niche products may hit the market in a few years.

One possible area of ‚Äč‚Äčapplication deserves special mention: electronics based on graphene. As described, the charge carriers in the material move at high speed and lose relatively little energy through collisions with the atoms in the crystal lattice. This should enable the construction of so-called ballistic transistors, which switch much faster than conventional devices.

Even more fascinating is the prospect of using graphs to extend the validity of an empirical rule that the electronics pioneer Gordon Moore formulated some 40 years ago. According to this, the number of transistors that can be accommodated in a certain area doubles every 18 months. The inevitable end of this advancing miniaturization has often been prematurely prophesied. Thanks to its remarkable stability and electrical conductivity even in the nanometer range, graphene may be suitable for transistors that measure well below ten nanometers and possibly consist of just a single benzene ring. Even complete integrated circuits that can be "cut out" from a single graphene plate would be conceivable.

The material, which is only one atom thick, certainly has a great future as a starting point for innovative commercial products as well as a mini-laboratory for the detection of exotic quantum properties. One can only be amazed that all this abundance and complexity has been hidden in every pencil stroke for centuries.