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For a brief time in Portland, Oregon,this past spring, thousands
of physicistsmoved from session to session at theannual March
meeting of the American
Physical Society (APS) on the lookout for thenext big thing.
It was a talent search not unlike the one thatunfolds every
night in the bars and converteddance halls of Portlands famous
music scene,where locals listen for the next big sound.
Thephysicists quest is a lot harder, though. Trendsin music come
and go, but the disciplines thatdominate the APS March meeting
suchas optics, electronics and condensed-matter
physics are rooted in the original theoriesof quantum mechanics,
which were more-or-less completed in the 1930s. When it comes
todescribing how light and matter behave, onlya few phenomena have
emerged since then tobecome the physics equivalent of
superstars.
At this years APS meeting, however, the hall-ways were filled
with talk of a promising new-comer an eccentric class of materials
knownas topological insulators. The most strikingcharacteristic of
these insulators is that theyconduct electricity only on their
surfaces. Thereasons are mathematically subtle so muchso that one
physicist, Zahid Hasan of Princ-
eton University in New Jersey, tried to explainthe behaviour
using simpler concepts such as
superstring theory. (Its awfully beautiful stuff,he said
reassuringly.) Yet the implications arerich, ranging from practical
technology forquantum computing to laboratory tests ofadvanced
particle physics.
Hence the excitement. It is still too earlyto say whether
topological insulators are thenext big thing. But physicists are
auditioning
various formulations of the insulators in theirlabs, eager to
determine whether the materialcan live up to its many promises.
A topological insulator sounds simple
enough a block of material that lets electronsmove along its
surface, but not through itsinside. In fact, it is far from
straightforward.Ordinary metals conduct electrons all the
waythrough, whereas ordinary insulators dontconduct electrons at
all. A copper-plated blockof wood conducts only on the surface, but
thatis two materials, not one. The idea of a topo-logical insulator
is so strange that for a longtime, physicists had no reason to
believe thatsuch a material would exist.
Quantum danceThings changed in 2004, when Charles Kane, a
theoretical physicist at the University of Penn-sylvania in
Philadelphia, was studying sheetsof carbon called graphene. Kanes
calculationssuggested that electrons would move throughthis
one-atom-thick material in a way thatreminded him of the quantum
Hall effect:a phenomenon first observed in 1980. Thiseffect occurs
when electrons are confined tothin films of certain materials,
subjected tolarge electric and magnetic fields, and cooledto within
just a fraction of a degree aboveabsolute zero. At that point, the
ordinarilychaotic motion of the electrons gives way toa more
orderly collective behaviour governed
by quantum mechanics. The transition showsup in the laboratory
as a series of discrete
A new class of materials is poised to take condensed-matter
physics by storm.
Geoff Brumfiel looks at what is making topological insulators
all the rage.
J.
Burton
Electrons move along the surface of, but not through,
topological insulators such as bismuth selenide.
J.Seo/P.
rouShan/a.Y
azdani
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quantum steps in the capacity of the materialto conduct
electricity.
What Kane and his group saw in their
graphene calculations wasnt exactly the sameas the quantum Hall
effect. Even so, furtheranalyses showed that there might be
otherthin-film materials with similar behaviour.This time there
would be no need for hugeexternal magnetic fields or ultra-low
temper-atures to get the electrons moving in unison.Such a material
would produce the magneticfield from the nuclei of its own atoms
possibly even at room temperature.
These coordinated electrons would mostlyend up just spinning in
place. Intriguingly, how-ever, those at the edge of the thin film
wouldbe forced to skip along the boundary. The net
result would be that thin samples would conductelectricity along
the edge and only along theedge but in separate quantum steps,
similar tothose seen in the quantum Hall effect1.
The work of Kane and his colleagues gotnoticed almost
immediately. Joel Moore, a theo-rist at the University of
California, Berkeley, andhis co-workers built on Kanes calculations
toshow that three-dimensional blocks of materialwould also display
quantum effects2, althoughthe way electrons moved along the
surfacewould be more complex than in the flat sheetused by Kane.
Moore also gave the materials anew name. They were originally
termed novel
Z2 topological invariants by Kane, in refer-ence to the
quantum-mechanical propertiesthat cause the electrons to skip along
the edge.We got tired of typing that out, so we called ita
topological insulator, says Moore. I dontknow that that term is
particularly explanatory,but at least its short.
Meanwhile, Shoucheng Zhang at StanfordUniversity in Palo Alto,
California, and histeam were researching what types of real
mate-rial could be topological insulators. In mostmaterials, Zhang
realized, the link betweenelectrons and nuclei is too weak to
create atopological-insulating behaviour. But the link
gets stronger as the nuclei get heavier. In 2006,Zhang predicted
that one material in particular,a crystal made of the heavy
elements mercuryand tellurium, would be able to do the trick3.And
within a year, Laurens Molenkamp, aphysicist at the University of
Wrzburg in Ger-many, and his group had grown a thin layer ofmercury
telluride crystal and showed that itsconductance hopped from one
quantum valueto the next along the edge of the sample4.
The experiment by Molenkamp provedthat the theorists were onto
something, but byitself it didnt cause much excitement.
Mercurytelluride crystals are difficult to obtain they
have to be grown one layer at a time using alaborious process
known as molecular beam
epitaxy and they are not pure topologicalinsulators because they
conduct some electricityon their inside.
New compounds based around bismuth,which are simple to make and
cheap to workwith, have caused the field to take off. Whatgot so
many talks at the March meeting wasthe bismuth-based compounds,
says Hasan.Anybody can grow them, you can buy themoff the shelf,
and you dont need a high-puritycrystal to see the topological
effects.
Those effects go beyond the way electronsmove on the surface.
For example, all elec-trons are spinning in a quantum
mechanicalway. Usually, the spins are constantly knockedabout by
random collisionsand stray magnetic fields. But
spinning electrons on the sur-face of a topological insulatorare
protected from disruptionby quantum effects (for more,see page
323). This could makethe materials beneficial forspin-related
electronics, whichwould use the orientation of theelectron spin to
encode infor-mation, thereby opening up awhole new realm of
computertechnology.
Mathematical mimicry
Researchers also believe thatthe collective motions ofelectrons
inside topologicalinsulators will mimic sev-eral of the
never-before-seenparticles predicted by high-energy physicists.
Amongthem are axions, hypotheticalparticles predicted in the 1970s;
magneticmonopoles, single points of north and southmagnetism; and
Majorana particles mass-less, chargeless entities that can serve as
theirown antiparticles.
This mimicry is not entirely surprising.
Almost by definition, collective electronmotions can be
described by just a handful ofvariables obeying simple equations,
says FrankWilczek, a Nobel-prizewinning particle physicistat the
Massachusetts Institute of Technologyin Cambridge. There are only a
few kinds ofequations that you can write down that arereally
simple, he says. So topological-insula-tor theorists and particle
physicists have almostinevitably ended up in the same place.
Majorana particles could prove particularlyuseful for practical
quantum computing. Theidea is to perform calculations using the
laws ofquantum mechanics, which could make com-
puters much faster than the normal variety atcertain tasks such
as code-breaking. But the
fragile quantum states essential to their operationare easily
destroyed by jolts from the out-side environment. Majorana
particles would
spread quantum information across particles,making them far more
resistant to interfer-ence, says Kane. If Majorana particles
couldbe harnessed on the surface of a topologicalinsulator, this
would be big, he says.
The wealth of calculations, experiments andapplications offered
by topological insulators,together with their availability, have
given thefield a white-hot status at the moment as hasa certain
thirst for glory. Two variations of thequantum Hall effect have won
their discover-ers Nobel prizes, and some researchers think
that a Nobel awaits whoevercan contribute the most to the
growing field. Im not thinkingabout that at this point,
saysKane, but the competitivenesshas forced him to ensure
thatothers are aware of his work.I sort of feel like if I dont
assertmyself, then Im going to getburied, he says.
Yet trips to Stockholm aresome way off. Although sam-ples of
topological insulatorsare now easy to get hold of, moststill
contain impurities thatcause them to conduct electric-
ity on the inside, disrupting thestates on the surface.
Gettingthings perfect remains more ofan art than a science.
Further-more, some of the sought-aftereffects will require
topologi-cal insulators to be combinedwith more common materi-
als. To create Majorana particles, for example,topological
insulators will have to merge withsuperconductors. Many experiments
on howbest to do that are under way.
The results of these studies will determinewhether topological
insulators are more than a
one-hit wonder. Regardless, says Moore, thereis an undeniable
appeal in how the collectivebehaviour of electrons can lead to so
manywonderful things. Theres something aboutmany-particle quantum
mechanics that causesperfection to emerge out of imperfection,
hesays. Thats somewhat cheering as far as oureveryday lives are
concerned. Geoff Brumfiel is a senior reporter forNature
based in London.
1. Kn, C. L. & Ml, e. J. Phys. Rev. Lett.95, 146802
(2005).2. Moor, J. e. & Blns, L.Phys. Rev. B 75,121306
(2007).3. Brnvig, B. a., hugs, t. L., zng, S.-C. Science314,
17571761 (2006).4. Knig, M. et al. Science 318, 766770
(2007).
See News & Views, page 323, and Letters, page 343.
n
S h a
n n o n
Theres something
about many-particle
quantum mechanicsthat causes
perfection to emerge
out of imperfection.
Jol Moor
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