The infinitesimal perturbation will move the Fermi angle of refraction gives rise to focusing of light basic concept that physicists use to understand energy into either the upper or the lower band, by a simple slab of the material. He went on to show that a negative unusual nature of its electronic spectrum. equivalent carbon atoms, means that symme- velocities point in opposite directions, just as is Graphene is an ideal two-dimensional sys- try forbids the interaction and bands cross at the case for the valence electrons in the new tem, and interest in it is compounded by the the Fermi energy without creating a gap. But the peculiar hexagonal symmetry the magnetic (µ) and electric (ε) responses are and sophisticated experiments can be per- of graphene, in which the unit cell contains two negative, he showed that the group and phase formed on them. Under conditions in which both vidual sheets of graphene can be isolated (3) nology. Recently, it has been reported that indi- forming the basis for all semiconductor tech- tion of light. tively weak, however, so that graphite is easily with impurity atoms, creating two different In 1968 (1), Veselago investigated the propsheared, which is what makes it a good lubri- types of materials, p-type or n-type, essentially erties of a medium that showed negative refraccant. A semiconductor can be doped velocities to be oppositely directed. The bonding between the sheets is rela- semiconductor. vides the link with the optical effect of negaatom connected by three bonds to its neighHowever, graphene is neither metal nor tive refraction, which requires group and waves bors. This prosheets comprising planar hexagons, each duction band with a few electrons. making them insulators, unless the semicon- States in the valence band have a group velocIn graphite, carbon atoms are arranged as ductor is doped or heated so as to fill the con- ity antiparallel to the wave vector. The Fermi level lies in this gap, duction band by symmetry, there is a twist: high precision.

However, although achieved in a monolayer of graphite (graph- one another and split apart generating an the valence band is closely related to the conene) and exploited to focus electrons with energy gap. On the basis of theoretical results, the authors claim that the electron equivalent of negative refraction can be conductors, two energy bands interact with duction band of graphene. (Right) Computer simulation of electron charge density on graphene showing similar focusing. Light formerly diverging from a point source in the object plane is set in reverse and conareas in a potentially fruitful way.

(Left) Veselago’s lens: A negative refractive index medium (n = –1) bends light to a negative angle this issue (4) combines these two relative to the surface normal. Condensed matter physicists, on the other hand, are unraveling the unusual properties of graphene, a material that consists of single sheets of carbon atoms (3). In the world of optics, for example, researchers have been studying negative refraction, a phenomenon that allows “perfect” optical lenses (1, 2) that can focus light beams to extremely fine points. Hance or cleverness sometimes brings together two exciting research areas that otherwise would proceed along separate paths. The peculiar properties of graphene, which is neither semiconductor nor metal, may allow its electrons to be focused like light. If you wish to distribute this article to others, you can order high-quality copies for your colleagues, clients, or customers by clicking here. The title Science is a registered trademark of AAAS. Copyright 2007 by the American Association for the Advancement of Science all rights reserved. Science (print ISSN 0036-8075 online ISSN 1095-9203) is published weekly, except the last week in December, by the American Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005.

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