The recent surge of interest in the electronic properties of graphene—that is, isolated layers of graphite just one atomic layer thick—has largely been driven by the discovery that electron mobility in graphene is ten times higher than in commercial-grade silicon, raising the possibility of high-efficiency, low-power, carbon-based electronics. Scientists attribute graphene's surprising current capacity (as well as a number of even stranger phenomena) to the presence of charge carriers that behave as if they are massless, "relativistic" quasiparticles called Dirac fermions. Harnessing these quasiparticles in real-world carbon-based devices, however, requires a deeper knowledge of their behavior under less-than-ideal circumstances, such as around defects, at edges, or in three dimensions—in other words, in graphite. At the ALS, a team of researchers using angle-resolved photoemission spectroscopy (ARPES) have now produced the first direct evidence of massless Dirac fermions in graphite coexisting with quasiparticles of finite effective mass and defect-induced localized states.

Photoemission geometry and crystallographic structure of two graphene layers.

An electron moving through a conventional solid is often described as having a small but finite effective mass (m*) that takes into account the drag on its momentum from the surrounding crystal lattice as well as from interactions with other particles. The energy (E) of such an electron depends quadratically on its momentum (p), as given by the equation E = p²/2m*. In graphene, however, it has been discovered that electrons behave as if they are massless, "relativistic" particles (like photons traveling in free space at the speed of light) that exhibit a linear dispersion relationship given by the equation E = vk, where the wavenumber (k) represents momentum and the Fermi velocity (v) stands in for the speed of light. Because these electrons obey the Dirac equation—a description of fermions (e.g., electrons) that combines quantum mechanics with special relativity—they are called Dirac fermions.

Dirac fermions have been invoked recently to explain various peculiar phenomena in condensed-matter physics, including the novel quantum Hall effect in graphene, the magnetic-field-driven metal–insulator-like transition in graphite, superfluidity in ³He, and the exotic pseudogap phase of high-temperature superconductors. Despite their proposed key role in these highly interesting systems, direct experimental evidence of Dirac fermions has been limited. Furthermore, although several experiments have seemed to point to the existence of these relativistic particles in graphite, no direct observations have previously been reported.

At ALS Beamlines 12.0.1 and 7.0.1, researchers studied the nature of quasiparticles in single-crystal graphite by performing high-resolution ARPES experiments. ARPES is unique in that it allows us to directly probe electronic structure using both energy and mometum information not accessible through any other type of measurement. The results provide the first direct experimental proof that Dirac fermions indeed exist in the low-energy dynamics of graphite. ARPES intensity maps taken near corner H of the Brillouin zone (BZ) show the linear dispersion characteristic of Dirac fermions. Near BZ corner K, however, a parabolic dispersion indicates the coexistence of quasiparticles with finite effective mass, probably due to interactions between the different graphene layers.

Left: Diagram of the Brillouin zone of graphite. Center: Dirac fermions in momentum space near corner H of the Brillouin zone are characterized by a sharply linear Λ-shaped dispersion relation, similar to that found in graphene. Right: As a result of interlayer interactions, other regions of momentum space (near corner K) display a parabola-shaped dispersion, signifying the existence of quasiparticles with finite mass whose energy is quadratically dependent on momentum.

The experiment also revealed the presence of defect-induced localized states in the proximity of zigzag edge structures, indicating that graphite's electronic structure is strongly affected by the network structure of sp² carbon, as is the case for fullerenes and carbon nanotubes. This kind of information will be of fundamental importance if we eventually hope to engineer graphite down to the nanometer scale for possible use in electronic devices.

Left: A typical graphite layer, in which honeycomb structures coexist with zig-zag edge regions. Right: Intensity maps as a function of energy and momentum. The top map shows the parabolic dispersion intrinsic to graphite. The bottom map, measured near a zig-zag edge, shows a large electron pocket due to defect-induced states.

Graphite is a unique system in which three different types of excitations—massless Dirac fermions, quasiparticles with finite effective mass, and defect states—coexist. These special ingredients add an exotic flavor to the low-energy electron dynamics of this familiar yet surprising material that combines the realms of nonrelativistic condensed matter physics on the one hand and relativistic particle physics on the other.

Research conducted by S.Y. Zhou, C.D. Spataru, D.-H. Lee, S.G. Louie, and A. Lanzara (University of California, Berkeley, and Berkeley Lab); G.-H. Gweon (University of California, Berkeley); J. Graf and A.V. Federov (Berkeley Lab); R.D. Diehl (Pennsylvania State University); and Y. Kopelevich (Universidade Estadual de Campinas, Brazil).

Research funding: National Science Foundation; U.S. Department of Energy, Office of Basic Energy Sciences (BES); and Laboratory Directed Research and Development Program of Berkeley Lab. Operation of the ALS is supported by BES.

Publication about this research: S.Y. Zhou, G.-H. Gweon, J. Graf, A.V. Federov, C.D. Spataru, R.D. Diehl, Y. Kopelevich, D.-H. Lee, S.G. Louie, and A. Lanzara, "First direct observation of Dirac fermions in graphite," Nature Physics 2, 595 (2006).