Graphene: semimetal, not semiconductor, insulator, or metal

July 15, 2011 — US Department of Energy’s Lawrence Berkeley National Laboratory (Berkeley Lab) researchers have used the Lab’s Advanced Light Source (ALS) to determine that graphene is a special kind of semimetal.

"Graphene is not a semiconductor, not an insulator, and not a metal," explained David Siegel, graduate student in Berkeley Lab’s Materials Sciences Division (MSD) and a member of Alessandra Lanzara’s group in the Department of Physics at the University of California at Berkeley.

An ALS beamline 12.0.1 probed a specially prepared sample of graphene with angle-resolved photoemission spectroscopy (ARPES) to observe how undoped graphene behaves near the Dirac point, a feature of graphene’s band structure.

Semiconductors have bandgaps (an energy gap between the electron-filled valence band and the unoccupied conduction band). Graphene’s valence and conduction bands are represented by two Dirac cones with touching points that cross linearly at the Dirac point (see the figure). In undoped graphene, the valence band is completely filled and the conduction band is completely empty.

The ARPES experiment measured a slice through the cones by directly plotting the kinetic energy and angle of electrons that fly out of the graphene sample when they are excited by the ALS x-ray beam. The emitted electrons hit the detector and build a spectrum, a picture of the Dirac cones.

The electron interaction in undoped graphene excludes graphene from being a metal. The sides of the cone (or legs of the X, in an ARPES spectrum) develop a distinct inward curvature, indicating that electronic interactions are occurring at increasingly longer range — up to 790 angstroms apart — and lead to greater electron velocities. These are unusual previously unknown manifestations of renormalization.

To study graphene without the inteference caused by a substrate, Siegel’s team developed "quasi-freestanding" graphene: Driving silicon out of a silicon carbide substrate to build a relatively thick layer of graphite. Adjacent layers of graphene in the thick graphite sample are rotated with respect to one another, so that each layer in the stack behaves like a single isolated layer.

Landau’s Fermi-liquid theory
The Soviet physicist Lev Landau and the Italian and naturalized-American physicist Enrico Fermi developed a theory of solids that is relevant to this experiment. While individual electrons carry charge, even in a metal they can’t fully be understood as simple, independent particles. Because they are constantly interacting with other particles, the effects of the interactions have to be included; electrons and interactions together can be thought of as “quasiparticles,” which behave much like free electrons but with different masses and velocities. These differences are derived through the mathematical process called renormalization.

Landau’s Fermi liquid is made up of quasiparticles. Besides describing features of electrons plus interactions, Fermi liquids have a number of other characteristic properties, and in most materials the theory takes generally the same form. It holds that charge carriers are “dressed” by many-body interactions, which also serve to screen electrons and prevent or reduce their longer-distance interactions.

"Undoped graphene really does differ from what we expect for a normal Fermi liquid, and our results are in good agreement with theoretical calculations," reported Siegel. Unscreened, long-range interations among electrons demonstrate this abnormal behavoir.

"Many-body interactions in quasi-freestanding graphene," by David A. Siegel, Cheol-Hwan Park, Choongyu Hwang, Jack Deslippe, Alexei V. Fedorov, Steven G. Louie, and Alessandra Lanzara, appears in Proceedings of the National Academy of Sciences, online at http://www.pnas.org/content/early/2011/06/20/1100242108.abstract

Siegel, Deslippe, Louie, and Lanzara are members of Berkeley Lab’s Materials Sciences Division and the UCB Department of Physics. Park is with UCB’s Department of Physics, Hwang is with the Materials Sciences Division, and Fedorov is with the Advanced Light Source. This work was supported by the National Science Foundation and the U.S. Department of Energy’s Office of Science.

In the figure below, the conventional Dirac cones of graphene are drawn, with straight sides (left) indicating a smooth increase in energy. An ARPES spectrum near the Dirac point of undoped graphene (sketched in red at right) exhibits a distinct inward curvature, indicating electronic interactions occurring at increasingly longer range and leading to greater electron velocities.

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