INSIGHTS | PERSPECTIVES
By D. N. Basov1 and M. M. Fogler2
High-temperature superconductivity, unconventional magnetism, and charge-ordered states are examples of the spectacular properties that arise in solids through many-body effects, a consequence of electrons strongly interacting with one another and with the crystal lattice. In a seminal contribution, Landau
introduced quasiparticles, objects that behave in many ways as free electrons but with
velocities and masses altered or “
renormalized.” Information about the renormalization
is encoded, for example, in optical properties
of materials (1). The majority of optical studies have focused on response functions that depend on frequency v,
but dependence on momentum q,
which is equally valuable, has remained beyond the reach of common spectroscopic tools. On page
187 of this issue, Lundeberg et al.
(2) developed a means to probe the
nonlocal or q-dependent electromagnetic response by harnessing
surface plasmon polaritons (
plasmons). Implications of the first results by Lundeberg et al. transcend
the studies of graphene, their
Plasmons can be regarded as
coupled oscillations of electron
density and electromagnetic field
at frequency v0. Imaging of plas-
monic waves in real space by
scanning near-field optical mi-
croscopy is well suited for prob-
ing the response functions of
two-dimensional (2D) materials,
including graphene (3). However,
investigation of many-body effects
in graphene by Lundeberg et al. de-
manded that the plasmon imaging
be done with low-frequency tera-
hertz radiation. They accomplished
this difficult task using a combina-
tion of near-field optics, scanned-
probe imaging, and photocurrent
measurements, as previously de-
scribed by the same collaborative
team (4). To study the plasmons, they fab-
ricated structures in which graphene was
separated from gold back gate electrodes by
insulating boron-nitride spacers only a few
nanometers in thickness.
The wavelength of plasmonic modes
measured in these experiments was nearly
300 times smaller than the wavelength
of terahertz photons. The corresponding
plasmon momentum was nearly 300 times
larger than the free-space photon momen-
tum v0/c, where c is the speed of light. The
reason for this large confinement factor is
the proximity of graphene to the back gate,
which screened Coulomb interactions and
forced the plasmon velocity to approach the
Fermi velocity nF of graphene quasiparticles
(see the figure). For these “slow” plasmons,
the many-body renormalization of the plas-
mon dispersion is more apparent than in
common graphene structures in which in-
teractions are not screened.
Remarkably, the plasmon dispersion v(q)
determined by Lundeberg et al. is in accord
with parameter-free theoretical calculations.
These calculations link the renormalized
plasmon dispersion to the “hourglass” shape
of the electronic bands in graphene (see the
figure, top), a salient product of many-body
interactions (5). By taking into account ad-
ditional dynamical correlations of the quasi-
particles, the authors achieved a near-perfect
agreement between the theory and
their plasmonic imaging data.
Ramifications of many-body
physics in graphene are de-
monstrably different from the
behavior of other complex and
synthetic conductors. Notably, the
theoretical discussion of many-
body physics in honeycomb car-
bon preceded the isolation of
graphene by almost a decade (6).
However, early measurements
at the rise of graphene research
seemed to suggest noninteracting
Dirac quasiparticles (7). Among
conspicuous exceptions were the
hints of nF enhancement at rela-
tively low carrier density inferred
from infrared spectroscopy (8).
The change in shape of the electron and hole bands from simple
Dirac cones to an hourglass when
interactions are present was firmly
established by transport experiments with high-mobility samples
(5). In contrast, electronic correlations in synthetic metals, such as
transition metal oxides, induce
“flattened” electronics bands (1), in
contrast to graphene’s hourglass-like renormalization. Likewise,
plasmons in graphene acquire
higher velocity because of many-body effects (2), unlike the response of correlated 2D synthetic
conductors, in which interactions
further slowdown plasmons (9).
The physical reason for intricate
differences of renormalization effect in graphene and other syn-
Plasmonic imaging is gaining momentum
1Department of Physics, Columbia University,
New York, N Y 10027, USA. 2Department of
Physics, University of California San Diego, La
Jolla, CA 92093, USA. Email: db3056@columbia.
Terahertz nanospectroscopy reveals many-body interactions in graphene
Dirac cone adopts
an hourglass shape.
Renormalized plasmon dispersions
Slow plasmons (3, 4) are prone to renormalizations by many-body interactions.
The net efect is enhanced plasmon velocity; c is the speed of light.
1 Photons in free space
disperse as v = cq.
2 In free-standing
disperse as v ; √q and
their velocity is reduced
compared to c.
3 Plasmons in graphene on
gold become nearly as slow
as the Fermi velocity nF.
4 Many-body efects
renormalize the velocity of
5 “Demon” modes have
yet to be seen.
v =cq v;√q
Electrons and plasmons in graphene
Lundeberg et al. used terahertz imaging of the surface of graphene near a gold
film to determine plasmonic dispersion (their frequency v versus momentum
q, where the slope is their velocity n).