We take it as given that all properties of matter originate from the laws of quantum mechanics. We rarely realize, however, that the true power of the nearly hundred-year-old quantum theory lies not in its ability to explain observed phenomena and properties of existing materials but on its so-called ‘predicting ability’—quantum theory can tell us how a new material will behave when it exists only in the mind of a scientist or on the virtual drawing board of a computer well before the material is created in the laboratory. The quantum theory’s predictive ability, for example, allows it to play the role of genetic engineering in the inanimate world.
Rapid development in the last 25 years in microelectronic devices has been accompanied by landmark changes in the spread of scientific information, preprint databases and open access journals being two examples of what the information revolutions has achieved. Together, the two developments have dramatically decreased the time it takes to turn a mathematical concept into a functional device based on that concept. This article tells the story of graphene, the material which I had an opportunity to work on directly soon after it was discovered in 2005, and also mentions a few other fascinating materials, developed in the last few years, that may soon show their potential.
Studying Solutions of the Dirac Equatation
In 1928 Paul Dirac wrote an equation describing the dynamics of an electron satisfying the demands of both quantum mechanics and Einstein’s special theory of relativity. The Dirac equation served as the foundation of the relativistic quantum theory, which could explain many phenomena that the non-relativistic theory had left unexplained.
At the same time, the relativistic quantum theory led to a series of results that conflicted with common sense, such as the existence of antimatter (positrons, for example, discovered in 1932 by Carl D. Anderson) and the Klein’s paradox (which claims that a beam of electrons incident on a potential barrier of infinite height is fully transmitted). Over the next few decades, many mathematicians and mathematical physicists studied solutions of the Dirac equation in different situations. A particularly popular version of the equation was the one describing electrons in the two-dimensional world, for which numerous exact solutions were available. Such studies seemed particularly removed from reality: our world is, after all, three-dimensional.
Hindered by a Dogma
Graphite and diamond, the only crystalline forms of carbon known in the mid-1980s, are three-dimensional. Graphite, which is the more commonly found form, consists of separate layers each only one atom thick, which have a honeycomb-like structure. The layers are relatively weakly bound to each other, and separate easily—a property that makes writing possible, the pencil simply transferring the material to paper. In 1984, Gordon W. Semenoff showed that electrons in a single layer of graphite (later called graphene) are described by the Dirac equation in its simplest form, valid for particles in a two-dimensional world that have no mass.