Scientists working at the Advanced Light Source (ALS) at the U.S.
Department of Energy's Lawrence Berkeley National Laboratory have discovered
striking new details about the electronic structure of graphene, crystalline
sheets of carbon just one atom thick. An international team led by Aaron Bostwick
and Eli Rotenberg of the ALS found that composite particles called plasmarons
play a vital role in determining graphene's properties.
"The interesting properties of graphene are all collective phenomena,"
says Rotenberg, an ALS senior staff scientist responsible for the scientific
program at ALS beamline 7, where the work was performed. "Graphene's
true electronic structure can't be understood without understanding the
many complex interactions of electrons with other particles."
A theoretical model of plasmaron interactions in graphene, sheets of carbon one atom thick.
The electric charge carriers in graphene are negative electrons and positive
holes, which in turn are affected by plasmons-density oscillations that
move like sound waves through the "liquid" of all the electrons
in the material. A plasmaron is a composite particle, a charge carrier coupled
with a plasmon.
"Although plasmarons were proposed theoretically in the late 1960s, and
indirect evidence of them has been found, our work is the first observation
of their distinct energy bands in graphene, or indeed in any material,"
Rotenberg says.
Understanding the relationships among these three kinds of particles-charge
carriers, plasmons, and plasmarons-may hasten the day when graphene can
be used for "plasmonics" to build ultrafast computers-perhaps
even room-temperature quantum computers-plus a wide range of other tools
and applications.
Strange graphene gets stranger
"Graphene has no band gap," says Bostwick, a research scientist
on beamline 7.0.1 and lead author of the study. "On the usual band-gap
diagram of neutral graphene, the filled valence band and the empty conduction
band are shown as two cones, which meet at their tips at a point called the
Dirac crossing."
Graphene is unique in that electrons near the Dirac crossing move as if they
have no mass, traveling at a significant fraction of the speed of light. Plasmons
couple directly to these elementary charges. Their frequencies may reach 100
trillion cycles per second (100 terahertz, 100 THz)-much higher than the
frequency of conventional electronics in today's computers, which typically
operate at about a few billion cycles per second (a few gigahertz, GHz).
Plasmons can also be excited by photons, particles of light, from external
sources. Photonics is the field that includes the control and use of light for
information processing; plasmons can be directed through channels measured on
the nanoscale (billionths of a meter), much smaller than in conventional photonic
devices.
And since the density of graphene's electric charge carriers can easily
be influenced, it is straightforward to tune the electronic properties of graphene
nanostructures. For these and other reasons, says Bostwick, "graphene
is a promising candidate for much smaller, much faster devices-nanoscale
plasmonic devices that merge electronics and photonics."
The usual picture of graphene's simple conical bands is not a complete
description, however; instead it's an idealized picture of "bare"
electrons. Not only do electrons (and holes) continually interact with each
other and other entities, the traditional band-gap picture fails to predict
the newly discovered plasmarons revealed by Bostwick and his collaborators.
The team reports their findings and discuss the implications in "Observations
of plasmarons in quasi-free-standing doped graphene," by Aaron Bostwick,
Florian Speck, Thomas Seyller, Karsten Horn, Marco Polini, Reza Asgari, Allan
H. MacDonald, and Eli Rotenberg, in the 21 May 2010 issue of Science, available
online to subscribers.
Graphene is most familiar as the individual layers that make up graphite, the
pencil-lead form of carbon; what makes graphite soft and a good lubricant is
that the single-atom layers readily slide over one another, their atoms strongly
bonded in the plane but weakly bonded between planes. Since the 1980s, graphene
sheets have been rolled-up into carbon nanotubes or closed buckyball spheroids.
Theorists long doubted that single graphene sheets could exist unless stacked
or closed in on themselves.
Then in 2004 single graphene sheets were isolated, and graphene has since been
used in many experiments. Graphene sheets suspended in vacuum don't work
for the kind of electronic studies that Bostwick and Rotenberg perform at ALS
beamline 7.0.1. They use a technique known as angle-resolved photoemission spectroscopy
(ARPES); for ARPES, the surface of the sample must be flat. Free-standing graphene
is rarely flat; at best it resembles a crumpled bedsheet.
Using electrons to draw images of composite particles
"One of the best ways to grow a flat sheet of graphene is by heating
a crystal of silicon carbide," Rotenberg says, "and it happens that
our German colleagues Thomas Seyller from the University of Erlangen and Karsten
Horn from the Fritz Haber Institute in Berlin are experts at working with silicon
carbide. As the silicon recedes from the surface it leaves a single carbon layer."
Using flat graphene made this way, the researchers hoped to study graphene's
intrinsic properties by ARPES. First a beam of soft x-rays from the ALS frees
electrons from the graphene (photoemission). Then by measuring the direction
(angle) and speed of the emitted electrons, the experiment recovers their energy
and momentum; the spectrum of the cumulative emitted electrons is transmitted
directly onto a two-dimensional detector.
The result is an image of the electronic bands created by the electrons themselves.
In the case of graphene, the picture is x shaped, a cross-sectional cut through
the two conical bands.
"Even in our initial experiments with graphene, we suspected that the
ARPES distribution was not quite as simple as the two-cone, bare-electron model
suggested," Rotenberg says. "At low resolution there appeared to
be a kink in the bands at the Dirac crossing." Because there really is
no such thing as a bare electron, the researchers wondered if this fuzziness
was caused by charge carriers emitting plasmons.
"But theorists thought we should see even stronger effects," says
Rotenberg, "and so we wondered if the substrate was influencing the physics.
A single layer of carbon atoms resting on a silicon carbide substrate isn't
the same as free-standing graphene."
The silicon-carbide substrate could in principle weaken the interactions between
charges in the graphene (on most substrates the electronic properties of graphene
are disturbed, and the plasmonic effects can't be observed). Therefore
the team introduced hydrogen atoms that bonded to the underlying silicon carbide,
isolating the graphene layer from the substrate and reducing its influence.
Now the graphene film was flat enough to study with ARPES but sufficiently isolated
to reveal its intrinsic interactions.
The images obtained by ARPES actually reflect the dynamics of the holes left
behind after photoemission of the electrons. The lifetime and mass of excited
holes are strongly subject to scattering from other excitations such as phonons
(vibrations of the atoms in the crystal lattice), or by creating new electron-hole
pairs.
"In the case of graphene, the electron can leave behind either an ordinary
hole or a hole bound to a plasmon-a plasmaron," says Rotenberg.
Taken together, the interactions dramatically influenced the ARPES spectrum.
When the researchers deposited potassium atoms atop the layer of carbon atoms
to add extra electrons to the graphene, a detailed ARPES picture of the Dirac
crossing region emerged. It revealed that the energy bands of graphene cross
at three places, not one.
Ordinary holes have two conical bands that meet at a single point, just as
in the bare-electron, non-interacting picture. But another pair of conical bands,
the plasmaron bands, meets at a second, lower Dirac crossing. Between these
crossings lies a ring where the hole and plasmaron bands cross.
"By their nature, plasmons couple strongly to photons, which promises
new ways for manipulating light in nanostructures, giving rise to the field
of plasmonics," Rotenberg says. "Now we know that plasmons couple
strongly to the charge carriers in graphene, which suggests that graphene may
have an important role to play in the merging fields of electronics, photonics,
and plasmonics on the nanoscale."
This research was supported by the DOE Office of Science.