S03E14: The Einstein Approximation

The hottest material in physics can be made with a pencil and Scotch tape.   That’s “hottest” in popularity, not temperature.  When a new, interesting, material is discovered, teams of physicists will race against each other to figure it out.   This decade’s material-of-the-century is graphene.

Graphene is merely chicken wire made with carbon atoms…chicken wire that is no thicker than a single atom.

Atomic chickenwire: A image of an actual sheet of graphene. Each little black dot is an empty space surrounded by six carbon atoms, forming a hexagon. (The width of the entire image is about one thouand times smaller than the width of a human hair.)

Carbon atoms love to form chains, as in alcohol, or even rings, as in chemicals found in gasoline.   Even more tangled-up connections of carbon create popular substances like diamonds and soot.  Physicists knew for decades that the existence of a single sheet of interconnected carbon atoms was possible, in principle.  But they also knew that such a structure could hardly be grown as a crystal since the structure tends to roll up and form three-dimensional bonds.

But only six years ago, in cutting-edge experiments (using Scotch tape and pencils), physicists succeeded in creating small quantities of graphene, smaller than a speck of dust.  Pencil lead, despite its name, has no “lead” in it.  Rather it is many layers of carbon sheets, like a deck of cards, stuck together called graphite (from the Greek “to write“).  The experimental heroes just stuck a little of the humble pencil graphite in a folded over piece of tape…and pulled, separating hundreds of atomic layers in two smaller stacks.   A student can repeat the process as many times as needed, until a single layer is  created.

The students transfer the single-sheet candidates from the tape to a silicon wafer for further study.  One of the researchers’  breakthroughs was to discover a quick way of identifying single layers from less interesting multiple layers.   Like oil floating on a puddle reflecting sunlight after the rain, the film thickness determines its color.   The thin, elegant, highly-sought single sheets of graphene appear pale pink, while their fatter cousins are blue.

The process produced perfect crystals, with no apparent defects.  Graphene would prove to be harder than diamond, yet flexible.  Graphene is not a metal, yet highly conductive.  Success having many mothers, after the discovery, claims of priority going back several decades have been staked.

Pity the poor condensed-matter theorists.  For over a century they have pushed pencils across their pads in search of new materials to propose.  Yet there graphene was, literally right under their noses, the entire time.

A few episodes ago, Sheldon took us in his mind to the fictional country of Flatland, where only two dimensions of motion are allowed.   Not at all fictional, graphene is a carbon Flatland with electrons fixed to move only in its two-dimensional world.  Lacking that one extra dimension turns most of the rules of materials on its head.  Graphene has captured the imagination of physicists with its potential applications.

High speed transistors:  The heart of computers and most other electronics are the fast switches called transistors.  The electrons in graphene are extremely mobile, able to cross thousands of carbon atoms without a single scatter.  So the idea, at least, has been put forward that graphene could be the basis of a new generation of higher speed, smaller integrated circuits.

Super-batteries:   Because its mass per area is as low as any imaginable material, graphene could revolutionize energy storage in batteries and the adoption of renewable energy.  Capacitors too, one of the basic building blocks of all electronics (they hold charge in circuits), could be replaced by far smaller graphene components.

Displays: Having the seemingly contradictory properties of transparency and conductivity at once, perhaps one day graphene sheets will produce large area touch-screens.  Now scientists only need discover what the iPad is good for.

Gas sensors:  Graphene’s low noise and high surface area could perhaps make it sensitive enough to detect even a single gas molecule adsorbed onto its surface causing a detectable step-like change in its electrical resistance.

Graphene could revolutionize electronics.

But what attracted Sheldon’s attention tonight is the theoretical description of electron motion in graphene.  By a mathematical coincidence, the equation that describes electron motion in graphene is almost the same as the fundamental equation of free electrons in relativistic quantum mechanics:  the famous Dirac Equation.   Because of the electrons’ interactions with the carbon nuclei, the electrons move as if they are massless.   So graphene can serve as a kind of laboratory for particle physics theorists, like Sheldon, to test their understanding of the mathematics they use every day under more abstract and less controllable conditions.

Graphene.  It’s the greatest thing since sliced pencil lead.