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October 31, 2007

 

 

Surprising QUASIPARTICLE Interactions in Graphene

Until now, the world’s electronics have been dominated by silicon, whose properties, while excellent, significantly limit the size and power consumption of today’s computer chips. In order to develop ever smaller and more efficient devices, scientists have turned their attention to carbon, which can be formed into nanostructures like nanotubes, whose properties can be tuned from metallic to semiconducting. However, using carbon nanotubes for complex circuits is nearly impossible because their location and functionality in devices cannot be controlled at will, making them a poor substitute for silicon. Graphene, however, does not have these limitations. This single sheet of carbon atoms that is the building block of carbon nanotubes, C60 molecules, and graphite turns out to have similar functionality but with the added benefit that it can be grown with conventional methods and patterned into devices.  Now, a group of scientists from Germany and the ALS, using angle-resolved photoemission spectroscopy (ARPES) at ALS Beamine 7.0.1, have succeeded in making the first measurement of the carrier lifetime in graphene over a wide energy scale and have found surprising new interactions that suggest new kinds of devices.

Graphene Electronic Band Structure

The atomic arrangement of graphene (background) is a honeycomb lattice of carbon atoms arranged in a two-dimensional plane. Its electronic band structure consists of two bands (yellow) that intersect only at a few points at the corners of a hexagonal Brillouin zone (red).

Particle Physics in Your Pencil

Quantum electrodynamics, or QED, is the theory of many-body interactions first invented in the 1950s by Richard Feynman and others to explain the interaction of relativistic electrons and photons. When applied to electrons in metals, the theory is complicated by the presence of additional particles such as phonons (vibrational excitations) and magnons (magnetic excitations). These interactions are important because they determine not only the electronic band structure of materials, but also such exotic properties as superconductivity, which represent the collective behavior of all the charges and nuclei. ARPES helps us to understand these behaviors by directly measuring the charge-scattering rates, which should allow theorists to narrow down the infinite possible scattering events to only the most important.

What makes things even more interesting is the fact that, while in ordinary materials the carriers behave more or less like free electrons, graphene’s charges behave truly relativistically—they are effectively massless. This means that graphene’s charges move like photons, with a "speed of light" 300 times slower than true photons. Therefore, graphene offers a new regime to study relativistic particle physics, not in large high-energy accelerators, but rather under ambient conditions in a solid.

Graphene is an ideal playground for exploring quantum electrodynamic (QED) interactions in a solid system. While other materials have shown signatures of electrons interacting with phonons (vibrational excitations) or magnons (magnetic excitations), the carriers in graphene show clear signatures of scattering from phonons, plasmons (collective oscillations of electron gas), and electron–hole pairs over a much wider energy scale (2500 millivolts) than is usually treated. 

The atomic arrangement and band structure of graphene has a most unusual topology consisting of two surfaces that touch each other at the so-called Dirac energy ED.  Normally, ED coincides with the Fermi level EF, but if these energies are separated, then huge changes to the number of charge carriers can be achieved. This separation is readily accomplished by dosing graphene with atoms or molecules, or by imposing an electric field in a gated device.  Since the many-body effects are sensitive to the charge density, graphene is a material in which the many-body interactions are readily tunable.

In the absence of many-body interactions, the bands appear conical. In reality, the charge carriers can decay by emitting plasmon or phonon excitations.  Phonons are vibrational excitations whose effects are well known on the band structure: electron–phonon coupling causes a kink in the bands near EF. Plasmons are density oscillations in the electron sea that carry their own momentum, and decay by plasmon emission is normally forbidden in two-dimensional metals. However, the special energy–momentum relationships of electrons and plasmons allow such decay events in graphene. This results in a kink feature at ED as well as EF.

 

Graphene "kinky" band structure

The band structure near the crossing energy at higher magnification, showing the effect of electron decays on the bands. The purple cones (left) represent the bands in the absence of decays (here carriers decaying by phonon, green, and plasmon, light blue, emissions are shown). The blue cones (right) represent the resulting "kinky" band structure.

In the experimental Fermi surface and band structures of the graphene film, one can see not only the predicted kinks at ED and EF, but also the associated changes in the band's sharpness, which confirm the presence of decay events.  Further information about the scattering came from varying the doping of the graphene film, which led to a tuning of the coupling strengths. 

Graphene monolayer grown on SiC

The Fermi surface (left) and horizontal/vertical band-structure cuts (middle/right) of a single monolayer of graphene grown on SiC. The presence of a finite circular Fermi contour shows that the as-grown samples are slightly doped (to about 1013 electrons/cm2). The band structure cuts show two kinks, at the Dirac crossing energy ED and at the optical phonon energy scale (indicated by the arrow), each of which have changes in the line width.

Understanding these decays is not just an academic subject; it is important because various forms of carbon have been shown to be superconducting, although the mechanisms are not completely clear. Furthermore, since plasmons can also couple to light, the demonstration of strong electron–plasmon coupling shows that novel carbon-based devices with both electronic and photonic functions might be possible.

Research conducted by A. Bostwick, T. Ohta, J. McChesney, and E. Rotenberg (ALS); T. Seyller and K. Emtsev (University of Erlangen, Germany);  and K. Horn (Fritz Haber Institute, Berlin).

Research Funding: U.S. Department of Energy, Office of Basic Energy Sciences (BES), and the Max Planck Society, Germany. Operation of the ALS is supported by BES.

Publication about this research: A. Bostwick, T. Ohta, Th. Seyller, K. Horn, and E. Rotenberg, "Quasiparticle dynamics in graphene," Nature Physics 3, 36 (2007).

 

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