Buckyball Monolayer Electronic Structure

The 1980s witnessed the discovery of fullerenes, whose novel properties have been intensively studied by experiment and theory but remain incompletely understood. Among the fullerenes, for example, the solid formed from C₆₀ molecules exhibits superconductivity at the relatively high temperature of about 40 K when doped with alkali metal atoms (only the high-T_c cuprate superconductors have higher transition temperatures). A Berkeley/Stanford/Italian collaboration working at the ALS has now reported angle-resolved photoemission measurements of C₆₀ (buckyball) monolayers doped with potassium. They were able to detect, for the first time, both the band structure and a Fermi surface, two classical electronic structure features that surprisingly survive in the presence of the strong interactions in this material.

Angle-resolved photoemission of a buckyball monolayer (K₃C₆₀) on a silver substrate yields features of the electronic structure, including the the two-dimensional intensity map in reciprocal (momentum or k) space of electrons with energy around the Fermi energy (Fermi surface).

Condensed matter scientists agree that, as a molecular solid, doped C₆₀ (fullerides) should have a narrow band width. This feature, combined with strong interactions, both between the electrons themselves (electron–electron) and between the electrons and the lattice vibration modes (electron–phonon), makes fullerides more challenging to study than other systems. Moreover, some even doubted whether a band dispersion of the type found in normal crystalline materials actually exists in fullerides because the strong interactions, whose energies are comparable to those of electrons, may disturb the electrons so much that bands could not form at all.

Electron–phonon interactions are of particular interest because they are a keystone of the BCS theory that explains the superconductivity in conventional metal superconductors. Whether high-T_c superconductivity in cuprates is due to electron–phonon interactions is still one of the most interesting physics problems nowadays, but such interactions are widely, if not universally, held to drive superconductivity in C₆₀ compounds.

To study this interesting but complex physics in the C₆₀ system, measurements of the energy band structure are of fundamental importance. Angle-resolved photoemission (ARPES) probes this structure directly by measuring the intensity, kinetic energy, and direction (momentum) of the photoelectrons excited by synchrotron radiation. However, after more than a decade of intense effort, direct observation of the momentum dependence (dispersion) of the electron bands remained elusive, owing to technical challenges imposed by both intrinsic features of the material and certain experimental effects.

Buckyball Shakedown

In solids, the stable configuration of atomic nuclei and their surrounding electrons is the one that minimizes the total energy. Stable doesn't mean frozen in place, however, as exemplified by vibrations of the nuclei around their equilibrium positions, which collectively give rise to wavelike patterns known as phonons that move through the solid. Normally, electrons move much faster than phonons, so at any moment, they can easily readjust to the vibrations. But if the electrons and phonons have similar energies and move at comparable speeds, they become much more closely linked. This intimate interaction between electrons and phonons is of far more than academic interest because it can confer special properties, such as superconductivity—the ability to transmit electricity without resistance.

A form of carbon discovered in 1985—molecules containing 60 carbon atoms—were named buckyballs because they resembled American architect R. Buckminster Fuller's geodesic domes. Physicists have expected that the range of energies accessible to electrons (band width) in buckyball solids would be comparable to that of phonons, though a decade of intensive effort had not yielded proof. Working at the ALS, Yang et al. have now provided the first direct experimental evidence for this assumption. Moreover, it turns out the band width is even smaller than expected, precisely because of electron–phonon interactions. Buckyballs are an ideal model test ground for investigating such complex phenomena and might also find technological applications.

Experimental angle-resolved photoemission data showing photoelectron intensity as a function of energy for several values of momenta (indicated by the green arrow). The red arrows point to the the conduction-band energy at each momentum. The blue arrows are phonon satellites.

The collaboration was able to overcome these difficulties in their experiments on ALS Beamline 10.0.1, where they determined the Fermi surface and band structure. The observed conduction band exhibits a small dispersion with an energy range of only 100 meV, in sharp contrast with the 500-meV peak width seen in conventional angle-integrated photoemission spectra from the same conduction band. This substantial difference suggests the existence of strong interactions that broaden the peak width in photoelectron spectra but do not seem to affect the electronic structure, which exhibits a robust dispersion and classical Fermi surface.

The team then turned to quantum mechanical calculations conducted at Berkeley Lab's National Energy Research Scientific Computing Center (NERSC). There, they calculated the band dispersion and compared the result to the experimental data. It turned out that the simulated band width was much larger than the experimental value, though the basic shapes are consistent. This difference was attributed to electron–phonon coupling.

Fulleride monolayers provide a rare testing ground for exploring key conceptual issues involving strong interactions in materials with novel properties. The persistence of a clear classical (quasiparticle) electronic structure in the presence of strong interactions may imply that the electronic properties rely more on localized features, a distinction that could also be very important in understanding novel behaviors in other materials, such as high-T_c superconductors. Further investigations are under way to reveal still more interesting and deeper physics in these molecular crystals.

The photoelectron-intensity map shows the energy-momentum dispersion (darker region is higher intensity). The band width (maximum energy below the Fermi energy) is 100 meV.

Research conducted by W.L. Yang, V. Brouet, and X.J. Zhou (Berkeley Lab and Stanford University); H.J. Choi, S.G. Louie, and M.L. Cohen (Berkeley Lab and University of California, Berkeley); S.A. Kellar, P.V. Bogdanov, A. Lanzara, and Z.-X. Shen (Stanford University); Z. Hussain (ALS); A. Goldoni (Sincrotrone Trieste, Italy); and F. Parmigiani (Università Cattolica del Sacro Cuore, Brescia, Italy).

Research funding: U.S. Department of Energy, Office of Basic Energy Sciences (BES); Office of Naval Research; and the National Science Foundation. Operation of the ALS is supported by BES.

Publication about this research: W.L. Yang, V. Brouet, X.J. Zhou, H.J. Choi, S.G. Louie, M.L. Cohen, S.A. Kellar, P.V. Bogdanov, A. Lanzara, A. Goldoni, F. Parmigiani, Z. Hussain, and Z.-X. Shen, "Band structure and Fermi surface of electron-doped C₆₀ monolayers," Science 300, 303 (2003).

ALSNews Vol. 238, February 25, 2004

Buckyball Monolayer Electronic Structure

Buckyball Shakedown

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