search and discovery

Graphene yields evidence of atomic collapse
A relativistic phenomenon predicted for highly charged nuclei has
been seen in a tabletop experiment.

Crommie’s Berkeley group had alreadybeen reﬁning the techniques needed todetect it.

S

Triggering collapse

ince the discovery that electrons
in graphene behave as massless
Dirac fermions (see P HYSICSTODAY, January 2006, page 21), thesingle-atom-thick material has become afertile playground for testing exotic predictions of quantum electrodynamics.
Graphene experiments have been usedsuccessfully to probe such relativistic
phenomena as Klein tunneling—theanomalous, unimpeded passage of electrons through a high potential barrier—and the fractional quantum Hall eﬀect(see PHYSICS TODAY, January 2010, page11). Now add to that list atomic collapse,
the spontaneous formation of electronsand positrons in the electrostatic ﬁeld of
a superheavy atomic nucleus. Although
the phenomenon has eluded detection
in collider experiments, its condensedmatter analogue was recently spotted ina collaborative eﬀort headed by MichaelCrommie (University of California,Berkeley) and Leonid Levitov (MIT).1

impurities are atoms that stick to thegraphene surface and acquire charge.”
In models of atomic collapse, suchcharge impurities are treated as atomicnuclei. Graphene itself is treated as thevacuum: Its relativistic electrons andholes are analogous to the virtual particles that populate the vacuum in quantum ﬁeld theories. Crucially, because theeﬀective ﬁne-structure constant—whichsets the strength of interaction between
charges—is large for graphene, theorists
predicted2 that the graphene version ofatomic collapse should occur at a criticalcharge much closer to 1 than to 170.
Crommie, an experimentalist, ﬁrst
learned of that prediction when he saw
Levitov present theoretical results at a2009 conference. “I asked him, ‘Is thissomething we can really see in an experiment?’” As it turned out, not only
does the collapse produce an experimentally observable signature, but

Levitov’s calculations suggested thatatomic collapse in graphene should
reveal itself as a telltale electronic resonance—a short-lived, quasi-bound electronic state whose energy lies near
the Dirac point, the point in energy–
momentum space where graphene’sconduction and valence bands meet.
Crommie’s lab specializes in making precision scanning tunneling microscopy
measurements, which can reveal suchresonances. In a typical experimental
setup,3 depicted in ﬁgure 1, a bias voltage
V is applied between a graphene monolayer and an STM tip. By measuring how
the tunneling current I varies with V, theresearchers can piece together a pictureof how the charge-carrier concentrationin the graphene monolayer varies withenergy and location. A gate electrodeallows the team to manipulate the levelof electron or hole doping in the sample.

Sparking the vacuum
Atomic collapse is thought to eﬀectively set a ceiling on the periodic table:
For any atom whose proton number exceeds some critical value—estimated to
be around 170—the Dirac equation
predicts that the Coulomb ﬁeld of thenucleus should be strong enough to create an electron–positron pair from thevacuum. The newly formed electron
falls inward and “decharges” the nucleus; its antimatter counterpart is ﬂung
outward. To see atomic collapse in anexperiment, however, one would ﬁrst
need to create an atom nearly 50% more
massive than the current record holder,element 118. Collision experiments designed to ﬂeetingly create the requisite
superheavy nuclei have yielded only
ambiguous results.
Around 2006, Levitov, Antonio
Castro Neto (Boston University and theNational University of Singapore), andother condensed-matter theorists independently began to explore a twodimensional analogue of the atomiccollapse problem. “Our interest at thetime was to understand how impurities
change graphene’s electrical properties,” recalls Castro Neto. “And weknew that the most important kinds of12

May 2013

Physics Today

Bias voltage

AAmmeter
STM tipElectrodeGatevoltage

50 µm
Graphene
Silicon dioxide
SiliconGraphene atop boron nitride flake

Figure 1. A scanning tunneling microscopy (STM) setup used to measuregraphene’s local density of states. The monolayer graphene sample (purple)is deposited atop flakes of boron nitride to improve the uniformity of thebackground charge distribution. From variations in the measured current as afunction of bias voltage, one can infer the sample’s local density of states. Whenthe graphene is configured atop silicon dioxide and silicon sublayers, its chargecarrier doping can be manipulated with a gate voltage. (Adapted from ref. 3.)
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a3.0
Dirac point
2.5
2.0

dI/dV

To improve the uniformity of the background charge distribution, the teamdeposits their graphene samples atopboron nitride ﬂakes.
Although able to detect even the mostsubtle electronic hints of atomic collapse,
the researchers still faced the nontrivial
task of creating an impurity of suﬃcientcharge to see the eﬀect. In principle, asingle adsorbed atom with charge +eshould lie at or near the predicted
threshold for atomic collapse. But inpractice, that charge is heavily screenedby the electrons in the boron nitride substrate. “Reaching the critical charge
threshold turned out to be harder than
we thought,” Crommie says. “It became
obvious that we’d need to collect several
charge impurities together.”
There, too, the team encountered astumbling block. Single-atom impurities tend to nestle into the potential
wells of the graphene hexagons, so once
they’ve latched onto the material’s surface, they can’t always be easily repositioned. That was the case for calcium
atoms, an otherwise promising form of
charge impurity that the team used inearly trials. Eventually, the researchers
ﬁgured out that by heating the Ca impurities they could get the atoms toform movable dimers. Crommie’s students Yang Wang and Dillon Wong devised a way to use an STM tip to nudge
the dimers into clusters of as many asﬁve; each dimer carries a charge of +e,
so in essence, the team was able to build
the charge-impurity equivalent of aboron nucleus.
A ﬁve-dimer cluster turned out to be
more than suﬃcient to see atomic collapse. As illustrated by the orange curve
in ﬁgure 2a, STM spectra collected withthe tip positioned far away from such acluster are typical of what one would
ﬁnd in the absence of impurities. (Thequantity dI/dV plotted in the ﬁgureroughly corresponds to the chargecarrier local density of states.) The spectrum has the expected minimum at theDirac point—where, in principle, thematerial should be free of charge carriers. The increases in the local density ofstates above and below the Dirac point
reﬂect the introduction of conductionband electrons and the formation ofholes, respectively. The Dirac point isshifted from V = 0 due to an applied
gate voltage that prepopulates the sample with holes; the bandgap-like feature, roughly 0.2 eV wide and centeredat V = 0, is an artifact of phonon-assistedtunneling.
Unlike spectra collected far from thecluster, those collected with the tip po-

1.5
1.0
0.5
0.0
−0.6

3.7 nm
4.6 nm
5.5 nm
7.3 nm18.9 nm

−0.4

−0.2

0.0

0.2

BIAS VOLTAGE (eV)b0.4

Figure 2. Atomic collapse
in graphene. (a) A resonance(indicated by the red arrow)
just below the voltage
corresponding to the socalled Dirac point indicatesthe onset of collapse. (Here,dI/dV, the change in tunneling current with respect tobias voltage V, reflects the0.6 electronic local density ofstates; the bandgap-likefeature centered at V = 0
is an artifact of phononassisted tunneling.) Spectra
were collected with a scanning tunneling microscopy
tip at varying distances froma cluster of five positively
charged calcium dimers. The
resonance, indicative of ashort-lived bound electronicstate, appears at distancesless than about 10 nm.
(b) In a spatial map of theresonance intensity, thelocalized bound state isvisible as an orange halo.
(Adapted from ref. 1.)

5 nm

sitioned within about 10 nm of thedimers exhibit a sharp resonance at V
just below the Dirac point and show
hints of further oscillations at higher V.
The sharp resonance corresponds tothe predicted quasi-bound electronic
state—the quantum mechanical equivalent of a classical, spiral trajectory toward the charge impurity. In the spatial
map of the resonance’s intensity shownin ﬁgure 2b, that quasi-bound state isvisible as an orange halo surrounding
the ﬁve Ca dimers.
“Very few labs in the world could
have pulled this oﬀ,” comments CastroNeto. “From the perspective of newphysics, this is one of the most important graphene experiments since the2005 measurement of the quantum Halleﬀect.”

has implications for the miniaturizationof graphene-based electronics. Conceivably, a tiny gate electrode, shrunk down
to nanoscale proportions and charged
by an external power source, could giverise to atomic-collapse states like thoseseen by Crommie and company.
Eventually, researchers may be able
to harness that eﬀect. “By understanding and manipulating the atomiccollapse states,” Crommie says, “it may
be possible in the future to create new
types of device functionality at thenanoscale, similar to quantum dots andtransistor-like behaviors.” As for what’s
next, Crommie and his coworkers plan
to construct lattices of charged impurities to study how atomic-collapse statesinteract with one another.
Ashley G. Smart

Going small, thinking big

References

Besides potentially shedding light on
fundamental questions regarding thestability of matter, the discovery thatmodestly charged impurities can produce exotic electronic states in graphene

1. Y. Wang et al., Science (in press).
2. A. V. Shytov, M. I. Katsnelson, L. S. Levitov, Phys. Rev. Lett. 99, 246802 (2007); V. M.
Pereira, J. Nilsson, A. H. Castro Neto,Phys. Rev. Lett. 99, 166802 (2007).
3. R. Decker, Nano Lett. 11, 2291 (2011).

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Physics Today

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