The quantum pathways in Raman scattering are optically stimulated electronic excitations only possible if the initial electronic state is filled and the final state is empty (top). As pathways are removed by doping the graphene and lowering the Fermi energy (bottom), light from scattering may increase or decrease, depending on whether the removed pathways interfere constructively or destructively with the remaining pathways. Credit: Lawrence Berkeley National Laboratory
Scientists at Lawrence Berkeley National Laboratory (Berkeley Lab) and the Univ. of California
have learned to control the quantum pathways determining how light scatters in graphene.
Controlled scattering provides a new tool for the study of this material, and
may point to practical applications for controlling light and electronic states
in graphene nanodevices.
The research team, led by Feng Wang of Berkeley Lab’s Materials Sciences
Division, made the first direct observation, in graphene, of so-called quantum
interference in Raman scattering. Raman scattering is a form of inelastic light
scattering. Unlike elastic scattering, in which the scattered light has the
same color as the incident light, inelastically scattered light either loses
energy or gains it.
Raman scattering occurs in graphene and other crystals when an incoming
photon, a particle of light, excites an electron, which in turn generates a
phonon together with a lower-energy photon. Phonons are vibrations of the
crystal lattice, which are also treated as particles by quantum mechanics.
Quantum particles are as much waves as particles, so they can interfere with
one another and even with themselves. The researchers showed that light
emission can be controlled by controlling these interference pathways. They
present their results in a forthcoming issue of Nature.
quantum interference, in life and in the lab
“A familiar example of quantum interference in everyday life is anti-reflective
coating on eyeglasses,” says Wang, who is also an assistant professor of
physics at UC Berkeley. “A photon can follow two pathways, scattering from the
coating or from the glass. Because of its quantum nature it actually follows
both, and the coating is designed so that the two pathways interfere with each
other and cancel light that would otherwise cause reflection.”
Wang adds, “The hallmark of quantum mechanics is that if different paths are
non-distinguishable, they must always interfere with each other. We can
manipulate the interference among the quantum pathways that are responsible for
Raman scattering in graphene because of graphene’s peculiar electronic
In Raman scattering, the quantum pathways are electronic excitations, which
are optically stimulated by the incoming photons. These excitations can only
happen when the initial electronic state is filled, and the final electronic
state is empty.
Quantum mechanics describes electrons filling a material’s available electronic
states much as water fills the space in a glass: the water surface is called
the Fermi level. All the electronic states below it are filled and all the
states above it are empty. The filled states can be reduced by doping the
material in order to shift the Fermi energy lower. As the Fermi energy is
lowered, the electronic states just above it are removed, and the excitation
pathways originating from these states are also removed.
“We were able to control the excitation pathways in graphene by electrostatically
doping it—applying voltage to drive down the Fermi energy and eliminate
selected states,” Wang says. “An amazing thing about graphene is that its Fermi
energy can be shifted by orders of magnitude larger than conventional
materials. This is ultimately due to graphene’s two-dimensionality and its
unusual electronic bands.”
The Fermi energy of undoped graphene is located at a single point, where its
electronically filled bands, graphically represented as an upward-pointing
cone, meet its electronically empty bands, represented as a downward-pointing
cone. To move the Fermi energy appreciably requires a strong electric field.
A flake of graphene was grown on copper and transferred onto an insulating substrate of silicon dioxide. The Fermi energy in the graphene was adjusted by varying the gate voltage on the overlying ion gel, which confines a strongly conducting liquid in a polymer matrix. Credit: Lawrence Berkeley National Laboratory.
Team member Rachel Segalman, an associate professor of chemical engineering
at UC Berkeley and a faculty scientist in Berkeley Lab’s Materials Sciences
Division, provided the ion gel that was key to the experimental device. An ion
gel confines a strongly conducting liquid in a polymer matrix. The gel was laid
over a flake of graphene, grown on copper and transferred onto an insulating
substrate. The charge in the graphene was adjusted by the gate voltage on the
“So by cranking up the voltage we lowered the graphene’s Fermi energy,
sequentially getting rid of the higher energy electrons,” says Wang.
Eliminating electrons, from the highest energies on down, effectively
eliminated the pathways that, when impinged upon by incoming photons, could
absorb them and then emit Raman-scattered photons.
of interference, constructive and destructive
“People have always known that quantum interference is important in Raman
scattering, but it’s been hard to see,” says Wang. “Here it’s really easy to
see the contribution of each state.”
Removing quantum pathways one by one alters the ways they can interfere. The
changes are visible in the Raman-scattering intensity emitted by the
experimental device when it was illuminated by a beam of near-infrared laser
light. Although the glow from scattering is much fainter than the near-infrared
excitation, changes in its brightness can be measured precisely.
“In classical physics, you’d expect to see the scattered light get dimmer as
you remove excitation pathways,” says Wang, but the results of the experimenter
came as a surprise to everyone. “Instead the signal got stronger!”
The scattered light grew brighter as the excitation pathways were reduced—what
Wang calls “a canonical signature of destructive quantum interference.”
Why “destructively?” Because phonons and scattered photons can be excited by
many different, non-distinguishable pathways that interfere with one another,
blocking one path can either decrease or increase the light from scattering,
depending on whether that pathway was interfering constructively or
destructively with the others. In graphene, the lower and higher-energy
pathways interfered destructively. Removing one of them thus increased the
brightness of the emission.
“What we’ve demonstrated is the quantum-interference nature of Raman
scattering,” Wang says. “It was always there, but it was so hard to see that it
was often overlooked.”
In a second observation, the researchers found yet another unexpected
example of inelastic light scattering. This one, “hot electron luminescence,”
didn’t result from blocked quantum pathways, however.
Feng Wang beside a diagram showing how lowering the Fermi energy eliminates quantum pathways in graphene (lower left). The upper plot reveals that when destructively interfering quantum pathways are blocked, Raman scattering intensity is strongly enhanced (pale blue vertical, labeled G). At the same scattering, and at specific values of the Fermi energy, the plot reveals “hot electron luminescence” (labeled H.L.). Credit: Lawrence Berkeley National Laboratory.
When a strong voltage is applied and the graphene’s Fermi energy is lowered,
higher-energy electron states are emptied from the filled band. Electrons that
are highly excited by incoming photons, enough to jump to the unfilled band,
thus find additional chances to fall back to the now-vacant states in what was
the filled band. But these “hot” electrons can only fall back if they emit a
photon of the right frequency. The hot electron luminescence observed by the
researchers has an integrated intensity a hundred times stronger than the Raman
The poet Robert Frost wrote of coming upon two roads that diverged
in a wood, and was sorry he could not travel both. Not only can quantum
processes take both roads at once, they can interfere with themselves in doing
The research team, working at UC Berkeley and at Berkeley Lab’s Advanced
Light Source, has shown that inelastic light scattering can be controlled by
controlling interference between the intermediate states between photon
absorption and emission. Manipulating that interference has enabled new kinds
of quantum control of chemical reactions, as well as of spintronic states, in
which not charge but the quantum spins of electrons are affected. Strongly
enhanced Raman scattering can be a boon to nanoscale materials research. Hot
luminescence is potentially attractive for optoelectronics and biological
research, in which near-infrared tags could be very useful.
“Likewise the phenomenon of hot electron luminescence, because it
immediately follows excitation by a probe laser, could become a valuable
research tool,” says Wang, “particularly for studying ultra-fast electron
dynamics, one of the chief unusual characteristics of graphene.”