Thanks to the 2010 Nobel Prize for physics, graphene is a hot topic. That doesn’t mean it’s a household word. Graphene is not like pencil lead, which most people know is graphite. (That may hold for another generation or two, pencils are disappearing into tiny niches.) Yet graphene is graphite. Same stuff, pure carbon, just arranged a little differently. In a way, graphene is merely a sheet, a flake, a thin layer of graphite. Yet that layer changes everything. That’s because graphene is a sheet of carbon one measly atom thick. This is why scientists think of graphene as existing in two dimensions.

Not only is graphene one atom thick, its atoms are arranged in a honeycomb pattern (hexagonal shapes). However, that’s it: Carbon atoms, arranged as hexagons on a tiny sheet one atom thick. It sounds like graphene is simple stuff, but what this simplicity does to the physics! Graphene has many unique properties, and scientists continue to find more.

One new finding, which is still a matter of mathematical theory, describes a unique property of graphene that may provide a more convenient way to study something currently approachable only with a massive atomic particle accelerator. A group of physicists led by Abdulaziz Alhaidari at the Saudi Center for Theoretical Physics (Dhahran, Saudi Arabia) have published a paper at arXiv [Dynamical mass generation via space compactification in graphene] showing mathematically that the fundamental particles in graphene (fermions), which have no mass in two dimensions, will effectively have mass if the graphene is simply rolled into a tube.

How, you may ask, does an obviously three-dimensional figure (a tube) have only one dimension for moving fermions? This is where the unique properties of graphene come in: Electrons flowing through the special structure of graphene (hexagons in a one atom thick layer) behave like electrons travelling in a vacuum close to the speed of light. This behavior is not described by the traditional mathematics (Schrodinger equation) but by the mass-less Dirac equation. How then can these electrons acquire mass?

What constitutes and creates mass is a subject of debate in physics, but a commonly held theory is that matter at the smallest scale (nanoscale or below) has compacted dimensions. Describing these compactified spaces in quantum mechanics uses equations that include mass – voila, that’s how mass arises. Alhaidari and colleagues looked at these equations and wondered how they would apply to graphene. What if the space dimensions of two dimensional graphene were compactified into one dimension? Looking at various forms for graphene, they decided that when a sheet of graphene is rolled (essentially this makes a carbon nanotube), the fermions travelling down the tube would behave as if they were in a single dimension.

Remember, this is all mathematics. The Saudi physicists are not writing about creating mass ‘out of nothing.’ They’re saying that a two-dimensional condition that can be described with a massless Dirac equation can be effectively turned into a somewhat simpler one-dimensional equation with a term for mass. They believe this is the condition of a graphene sheet rolled into a tube. Mathematically the approach could provide a somewhat easier to use framework for looking at some very difficult problems in relativistic physics.

The math and the physics are tantalizing for the specialists. For most of us, the take-away is how graphene is providing the stimulus for theorizing and experimentation on a very broad front. From electronics to quantum physics this seemingly simple substance is opening fresh pathways for enquiring minds.

While it probably won’t be easy, there is hope that graphene as a physical substance can be involved in experiments that provide verification (or not) for mathematical predictions. The hope comes from the combination of graphene’s unusual properties and the fact that anybody in any lab anywhere can acquire graphene, attach electrodes to it, and go to work. While it’s not exactly the old ‘500 monkeys typing eventually create Shakespeare,’ easy accessibility to experimental procedures increases the chance that somebody will do breakthrough work.

Of course, there’s also hope that insights gained from the mathematical and physical knowledge of graphene will have practical applications. Even physicists smile at that happy thought. Engineers are more likely to be skeptical about the leap from quantum and relativistic effects at the nanoscale to finding useful applications at the macro scale (human visible size). I suppose this means that it will be a while (if ever) before graphene becomes a household word. On the other hand, the possible applications of graphene are already real enough to attract investment. In the end it may not matter so much if graphene is truly a ‘wonder material’ but that it was the material which caused so many people in science and technology to wonder.