Undoped graphene isn’t a metal, semiconductor, or insulator but a semimetal, whose unusual properties include electron-electron interactions between particles widely separated on graphene’s honeycomb lattice—here suggested by an artist’s impression of Feynman diagrams of such interactions. Long-range interactions, unlike those that occur only over very short distances in ordinary metals, alter the fundamental character of charge carriers in graphene. Image: Caitlin Youngquist, Berkeley Lab Public Affairs |
Graphene was an object of theoretical speculation long before it was
actually made. Theory predicts extraordinary properties for graphene, but
testing the predictions against experimental results is often challenging.
Now researchers using the Advanced Light Source (ALS) at the U.S. Department
of Energy’s Lawrence Berkeley National Laboratory (Berkeley Lab) have taken an
important step toward confirming that graphene is every bit as unusual as
expected—perhaps even more so.
“Graphene is not a semiconductor, not an insulator, and not a metal,” says
David Siegel, the lead author of a paper in the Proceedings of the National
Academy of Sciences (PNAS) reporting the research team’s results. “It’s a
special kind of semimetal, with electronic properties that are even more
interesting than one might suspect at first glance.”
Siegel is a 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.
He and his colleagues used ALS beamline 12.0.1 to probe a specially prepared
sample of graphene with ARPES (angle-resolved photoemission spectroscopy) in
order to observe how undoped grapheme—the intrinsic material with no extra
charge carriers—behaves near the so-called “Dirac point.”
The Dirac point is a unique feature of graphene’s band structure. Unlike the
band structure of semiconductors, for example, graphene has no band gap—no gap
in energy between the electron-filled valence band and the unoccupied
conduction band. In graphene these bands are represented by two cones (Dirac
cones) whose points touch, crossing linearly at the Dirac point. When the
valence band of graphene is completely filled and the conduction band is
completely empty, the graphene can be considered undoped or charge neutral. It
is here that some of the interesting properties of graphene may be observed.
An ARPES experiment neatly measures 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 an X?ray beam from the ALS. A spectrum develops
as these emitted electrons hit the detector screen, gradually building up a
picture of the cone.
The way the electrons interact in undoped graphene is markedly different
from that of 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—distances of up to 790
A apart—and lead to greater electron velocities. These are unusual
manifestations, never seen before, of a widespread phenomenon called “renormalization.”
Experiment
versus theory
To understand the significance of the team’s findings, it helps to start with
their experimental set up. Ideally, measurements of undoped graphene would be
done with a suspended sheet of freestanding graphene. But many experiments
can’t be done unless the target is resting on a solid substrate, which can
influence the electronic properties of the layer on the surface and interfere
with the experiment.
Dirac cones of graphene are often drawn with straight sides (left) indicating a smooth increase in energy, but 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—one of the ways the electronics of semimetallic graphene differ from a metal’s. |
So Siegel and his colleagues decided to investigate a special kind of “quasi-freestanding” graphene, starting with a substrate of silicon carbide.
When heated, the silicon is driven out of the silicon carbide and carbon
gathers on the surface as a relatively thick layer of graphite. But 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.
“In solid-state physics one of the most fundamental questions one can ask
about a material is the nature of its charge carriers,” Siegel says. “For
ordinary metals, the answer can be described by the most powerful theory of
solids, known as Landau’s Fermi-liquid theory,” after the Soviet physicist Lev
Landau and the Italian and naturalized-American physicist Enrico Fermi.
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 “quasi-particles,”
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 quasi-particles. 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.
“Since the properties of so many materials are pretty much the same in a
generalized way, physicists are always interested in finding systems that
differ from a normal Fermi liquid,” says Siegel. “This is what makes our
results so exciting. Undoped graphene really does differ from what we expect
for a normal Fermi liquid, and our results are in good agreement with
theoretical calculations.”
Perhaps the most vivid example of the difference is the long-range
interaction among electrons in semi-metallic graphene, interactions which would
be screened in a normal metal. Siegel grants that there may be continuing
controversy about how exactly graphene should be expected to behave, “but our
main result is that we have confirmed the presence of these unscreened,
long-range interactions, which change the behavior of quasiparticles in
graphene in a fundamental way.”
