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SCIENCE
By D. E. FeldmanT
he standard model of particle phys-
ics classifies all elementary particles
as fermions or bosons. Fermions, like
electrons, avoid each other. Bosons,
like photons, can bunch together. The
classification rests on a fundamen-
tal spin-statistics theorem of quantum field
theory and keeps these two types of particles
distinct from each other. However, on page
173 of this issue, Bartolomei et al. ( 1 ) report
an observation of particles that are neither
bosons nor fermions.
The authors’ notable experiment in no way
disproves the standard model. Indeed, the
standard model deals with particles in three-
dimensional space at the highest accessible
energies. The experiment deals with electric
charges in two spatial dimensions at low tem-
peratures. According to theory ( 2 , 3 ), this type
of two-dimensional system in a high mag-
netic field can give rise to emergent anyon
quasiparticles. Anyons have the distinctive
feature that their charge can be less than the
charge of an electron e ( 3 ), making them the
smallest in terms of charge. The quantum
statistics of anyons is an even more interest-
ing property. Quantum statistics tells us what
happens when identical particles exchange
their positions or run in circles around each
other. Although bosons and fermions behave
quite differently when exchanged, they show
no interesting behavior when one particle en-
circles another. This is because all particles
return to where they started after a full cir-
cle. When one anyon encircles another, their
long-range statistical interaction has a non-
trivial effect ( 2 , 3 ).
Experimental observation of anyon statis-
tics is a major challenge. The most natural
approach is based on interferometry, which
forces anyons to run around each other.
Promising results arrived a decade ago ( 4 ),
but theoretical interpretation of interfer-
ometry data has been difficult. Evidence for
anyon statistics has unexpectedly come from
thermal transport ( 5 – 7 ), which revealed non-
Abelian anyons ( 2 , 3 ) that possess multiple lo-
cally indistinguishable quantum states. This
property makes these anyons ideal buildingblocks for a topological quantum computer
( 2 ), which would require fewer qubits than
conventional quantum computers that need
error correction. Abelian anyons have no lo-
cally indistinguishable states. However, the
thermal transport observations lacked the
direct experimental evidence that Bartolomei
et al. provide of Abelian anyon statistics.
The authors’ experiment implements a
theoretical proposal for an anyon collider ( 8 ).
The device resembles an elementary-particle
collider but is much smaller in size and oper-ates at much lower energies. Bartolomei et
al. built a GaAs/AlGaAs heterostructure that
confines electrons in two dimensions. The
heterostructure was placed in a strong per-
pendicular magnetic field. This field made
the bulk of the heterostructure a fractional
quantum Hall insulator that hosts anyons of
charge e/3. Chiral conducting channels also
formed along the edges of the heterostruc-
ture. These properties allowed the authors to
explore a collision of two anyons propagat-
ing along the edges ( 1 , 8 ). This was accom-
plished by creating two dilute beams of any-
ons at two quantum point contacts (QPCs).
Quantum tunneling in the form of charge-
e/3 quasiparticles occurs when electric
charge generated from two different sources
reaches the QPCs. The tunneling particlesreach a third QPC. This is when quantum
statistics enters the game, as the two anyons
approach the QPC from opposite sides (see
the figure). If the particles were fermions in-
stead, they would block each other from tun-
neling through the third QPC because identi-
cal fermions cannot reside in the same place.
This means that any fluctuations in the fer-
mion currents collected in the drains would
be uncorrelated. If the particles were bosons,
this would cause a correlation between the
two drain currents as these particles bunch
together. Abelian anyons are intermediate in
their properties between fermions and bo-
sons. Therefore, some correlation of the two
drain currents is expected, although the spe-
cific details depend on the anyon statistics.
The authors’ experiment shows excellent
agreement with the theory ( 8 ) for charge-
e/3 (also called Laughlin) anyons ( 3 ). The
observations provide experimental sup-
port to long-predicted anyon statistics of
quasiparticles in fractional quantum Hall
liquids. They also bring with them a sur-
prise. Calculations in Rosenow et al. ( 8 )
were based on the simplest model of edge
channels (called the chiral Luttinger liquid
model), which often fails to quantitatively
describe experimental data ( 3 ). It is tempt-
ing to think that the observed signature
of anyon statistics has a deep reason that
goes beyond a particular model. Indeed,
this happens with a related nonequilibrium
fluctuation-dissipation theorem, which was
first discovered in the simplest model but
applies very generally ( 9 ).
Extending the experiment to other types
of Abelian and non-Abelian anyons would be
of great interest, as would be other probes of
anyon statistics. Recent progress includes a
new approach to interferometry ( 10 ) and the
extension of the thermal conductance tech-
nique to graphene ( 11 ). Such advances may
eventually contribute to the development of
topological quantum computing. Anyons are
also of interest for answering very basic ques-
tions about quantum matter. jREFERENCES AND NOTES- H. Bartolomei et al., Science 368 , 173 (2020).
- C. Nayak et al., Rev. Mod. Phys. 80 , 1083 (2008).
- M. Heiblum, D. E. Feldman, arXiv:1910.07046 [cond-mat.
mes-hall] (2019). - R. L. Willett, L. N. Pfeiffer, K. W. West, Proc. Natl. Acad. Sci.
U.S.A. 106 , 8853 (2009). - M. Banerjee et al., Nature 545 , 75 (2017).
- M. Banerjee et al., Nature 559 , 205 (2018).
- Y. Kasahara et al., Nature 559 , 227 (2018).
- B. Rosenow, I. P. Levkivskyi, B. I. Halperin, Phys. Rev. Lett.
116 , 156802 (2016). - C. Wang, D. E. Feldman, Phys. Rev. Lett. 110 , 030602
(2013). - J. Nakamura et al., Nat. Phys. 15 , 563 (2019).
- S. K. Srivastav et al., Sci. Adv. 5 , eaaw5798 (2019).
ACKNOWLEDGMENTS
This work was supported by NSF grant DMR-1902356.
10.1126/science.abb3552PHYSICSThe smallest particle collider
A new experiment finds direct evidence for anyons in a
semiconductor heterostructure
Brown Theoretical Physics Center and Department of
Physics, Brown University, Providence, RI 02912-1843, USA.
Email: [email protected]Electron source 2QPC3
D3QPC1QPC2Electron source 1D410 APRIL 2020 • VOL 368 ISSUE 6487 131Schematics of an anyon collider
The collider is a heterostructure that hosts a
quantum Hall liquid (yellow) in a strong magnetic
field. Electric charge from a source tunnels at the
quantum point contact (QPC) as an anyon (dashed
lines). Anyons colliding at QPC2 create current
fluctuations measured at points D3 and D4
characteristic of anyon statistics.