Using some of the world's most advanced photoelectron spectroscopy and computing techniques, Berkeley Lab scientists gained a more precise understanding of the electrical properties of fullerenes, those famous soccer-ball-shaped molecules comprised of 60 carbon atoms.

The team, which also includes researchers from Stanford University and Europe, obtained the first experimental measurement of the range of energies possessed by electrons, as a function of their momenta, in a single layer of carbon-60 molecules doped with additional electrons, a step that transforms the molecule into one of the best known superconductors, meaning it conducts electricity without resistance below a certain critical temperature.

	Buckyballs are soccer ball-shaped 60-atom clusters of pure carbon.

As expected in a molecular solid, they found that the electrons' energy-momentum range, also called the bandwidth, is quite narrow. But they were surprised by how narrow. And when they compared their measurements to theoretical calculations, they determined why.

"We knew the bandwidth was small. But our research reveals, experimentally, that it's even smaller than anticipated," says Steven Louie, a theoretical physicist in Berkeley Lab's Materials Sciences Division and a professor of physics at the University of California at Berkeley. "And we determined that the additional 50-percent reduction is consistent with the effects of electron-phonon interactions."

Their work, reported in the April 11, 2003, issue of Science, demonstrates how the electronic properties of fullerenes and similar molecules are affected by interactions between electrons and phonons — particles associated with atomic vibrations in a solid. This, in turn, will inform further research on other fullerene properties such as heat capacity and electron transport, possibly laying the groundwork for real-world applications.

A new form of carbon

Discovered in 1985 during experiments on carbon clusters using atomic beams, carbon-60 was named buckminsterfullerene, or buckyball, because it resembles American architect R. Buckminster Fuller's geodesic domes. Since then scientists have engineered giant fullerenes with as many as 960 carbon atoms, "buckybabies" with 32 atoms, and elongated structures such as nanotubes.

The molecules join diamond and graphite as the only forms of pure carbon, and have been heralded as stars in the burgeoning field of nanoscience, with potential uses as lubricants, drug delivery agents, and superconductors. In particular, researchers remain intrigued over the latter: when a carbon-60 solid is doped by inserting alkali atoms such as potassium into empty spaces within its crystal structure, it becomes superconducting at the relatively high temperature of about 40 degrees Kelvin. Because most conventional superconductors require temperatures at or below 20 degrees Kelvin, doped fullerenes offer a potentially easier way to incorporate zero resistance into electrical systems. Only the high-Tc cuprate superconductors have higher transition temperatures.

More research is needed however. Topping the to-do list is a precise measurement of the molecular solid's bandwidth. In other words, what is the energy-momentum range of the electrons, from the most tightly bound to the least tightly bound, in a given band? And what factors dictate this range? Based on theoretical calculations (and some indirect experimental evidence) conducted in the 18 years since its discovery, scientists know doped fullerene solids have a narrow bandwidth, and they know this is most likely due to interactions between electrons and phonons. But these theories lacked definitive experimental support.

To obtain this support, the team used Berkeley Lab's Advanced Light Source (ALS), a synchrotron that emits light in the x-ray region of the electromagnetic spectrum that is one billion times brighter than the sun. They subjected a doped carbon-60 monolayer to these extremely bright x-rays, which bombard the sample with photons. Electrons in the fullerene layer absorb the photons, gain energy, and bounce out of the layer. A detector then records the electrons' kinetic energies, which indicates the energy level they occupied in the layer. After recording a range of these electrons, the team produced the first photoemission measurement of a doped fullerene layer's bandwidth and band dispersion, which is the relationship between electron energy versus momentum.

Like running through water

This experimental bandwidth mirrored bandwidths derived from theoretical calculations, except for one important detail. It was 50 percent narrower. This means the electrons observed in the sample possessed less kinetic energy for a given momentum than expected. Or, put another way, they appeared to have more mass. The Berkeley Lab team knew this was an illusion; the electrons don’t possess more mass. Rather, the ALS data captured an interaction between electrons and some other particle that dulls the electrons’ energy-momentum and makes them appear heavier — much like a person trying to run in water will accelerate much more slowly, and seem to have more mass, than when they run on land.

But what acts like water in this case? What particle impairs the electrons’ energy-momentum? Earlier research pointed to one of two culprits: either electron-electron interactions, or electron-phonon interactions. The former phenomenon is easily explained. Because they repel one another, electron interactions make electrons appear heavier.

Phonons, however, are more difficult to grasp. Just as light can behave like a wave, as in an electromagnetic wave, or like a particle, as in a photon, so too can atomic vibrations that reverberate through a crystal structure. In classical physics, vibrations behave like sound waves, but at the quantum level, vibrations become particles called phonons. They’re created and absorbed as electrons push through the crystal lattice and distort the position of surrounding atoms. These distortions make the electrons appear heavier for a given momentum, the same way a person moves slower and feels heavier when attempting to run through water.

To determine if this phenomenon is responsible for the ALS experiment’s heavier-than-expected electrons, and narrowed bandwidth, the team turned to quantum mechanical calculations conducted at Berkeley Lab’s National Energy Research Scientific Computing Center (NERSC). There, they calculated the bandwidth and band dispersion of the carbon-60 monolayer using purely theoretical principles. They then compared the theoretical bandwidth, with and without electron-phonon effects, to the ALS-produced bandwidth, and got a nearly perfect match.

“It all falls together,” Louie says. “This experiment shows, at least for a monolayer on top of a metallic surface, that we don’t need additional phenomena like electron-electron interactions to explain the bandwidth. It also provides a quantitative understanding of the importance of electron-phonon interactions.”

The research is described in the Science paper, “Band Structure and Fermi Surface of Electron-Doped C60 Monolayers.” In addition to Louie, Berkeley Lab researchers Wan Li Yang and Zahid Hussain of the ALS, and Hyoungjoon Choi and Marvin Cohen of the Materials Sciences Division, contributed to the research. Other collaborators include Z. -X. Shen from Stanford University, and scientists from France’s Paris-Sud University, Italy’s Trieste Synchrotron, and Italy’s University Cattolica del Sacro Cuore.

Additional information

• "Band structure and Fermi surface of electron-doped C60 monolayers," by W. L. Yang, V. Brouet, X. J. Zhou, Hyoung J. Choi, Steven G. Louie, Marvin L. Cohen, S. A. Kellar, P. V. Bogdanov, A. Lanzara, A. Goldoni, F. Parmigiani, Z. Hussain, and Z.-X. Shen, Science, 11 April 2003

• More about Steven Louie

• More about fullerenes