joel moore- the next generation

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378 nature physics | VOL 5 | JUNE 2009 | www.nature.com/naturephysics

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within an advancing cell sheet, repatand colleagues have analysed the radialexpansion o cell colonies as a unctiono time. Surprisingly, they nd that largetraction orces are observed many cellrows behind the leading edge, suggestinga mechanical cooperation rom cell to cellover large distances within the cell sheet.As their results indicate long-range orcetransmission, this nding will undoubtedly

uel debates in the eld, especially on thequestion o the push or pull mechanism thatcould drive collective migration (Fig. 1b).

When thinking about cells moving as acohesive tissue, an important issue is theextent to which mechanical stress propagateswithin multicellular cohorts to controlmigration behaviour. Various in vivo andin vitro situations 7,8 suggest that extrinsiccues can drive the movement o tissues,not by acting directly on all members o

the group, but rather by instructing smallernumbers o peripheral leader cells that inturn seem to be responsible or the guidanceo naive ollowers. But it remains an openquestion whether the global motion iscoordinated by ‘leader’ cells pulling on cellsbehind or by internal pressure due to celldivision and proli eration that would expandcell sheets outwards. Additionally, othermechanisms could involve submarginal cellsthat extend ‘cryptic’ lamellipodia severalrows behind the wound margin o epithelialcell monolayers and thus could collectively drive cell-sheet movement 9.

Te direct measurement o physicalorces within advancing epithelial cellmonolayers provides some evidence todiscriminate between these various plausiblemechanisms. First, mapping the traction

orces in directions normal to and parallelto the ront edge at di erent locations

underlines that large traction orces exertedby cells on the substrate are observed araway rom the leading edge. Moreover,both traction distributions show non-Gaussian behaviours with exponential tails,independent o the distance rom the edge.It urther suggests that cells within the sheetshare a common mechanical behaviour witha long-range orce transmission. Te idea o leader cells moving outwards, normal to the

ree boundary, ‘dragging’ passive ollowersbehind them, is not sufcient to explain thiscomplex mechanical process.

Te propagation o physical orcesdepends on cell interactions not only withthe substrate but also with neighbouringcells. Tis implies a ‘tug o war’ between bothtypes o adhesion10. Physical signals rom thesubstrates tend to induce a migration o cellsaway rom each other, whereas a strongermechanical input rom cell–cell interactions

would drive them towards each other. Tusthe importance o cell–cell junctions in theorce transmission requires a cell sheet to

transmit physical orces in a cooperativeway. Consistent with these arguments,

repat et al.6 show that the average tractionstress exerted by cells on the substrate in thedirection perpendicular to the edge is notconcentrated at the leading edge but decaysslowly with the distance rom the edge overseveral cell diameters, keeping values largerthan zero. By applying Newton’s third lawat various distances rom the leading edgeo the cell sheet, they are able to use the

mechanical orce balance to calculate theaccumulated stress within the cell sheet.Tey show that this stress transmittedthrough cell–cell junctions increases as a

unction o the distance rom the edge. Tesecombined ndings clearly demonstrate thatguidance within tissues is due to a cohesive

and coordinated movement, and that thegrowth o the epithelial cell sheet is inducedby a global state o tensile stress (Fig. 1c).Interestingly, such a tensile stress rules outthe possibility o the build-up o an internalpressure due to cell proli eration that wouldpush neighbouring cells outwards.

A remaining question is how such a tensilestate is modulated by external cues, such asthe sti ness o the environment. As collectivecell migration and traction orces are a ectedby substrate rigidity 10,11, one would expectto observe changes in the value o the tensilestress with the sti ness, providing importantin ormation about the reciprocal modulationo tension induced by cell–cell and cell–ECMadhesions. Te study by repat et al. opensa promising possibility o testing the impacto mechanical stress on tissue remodellingand repair by dissecting the respectivecontributions o local and global orces. ❐

Benoit Ladoux is at the Laboratoire Matière et Systèmes Complexes (MSC), Université ParisDiderot, and CNRS, UMR 7057, Paris, France.e‑mail: benoit.ladoux@univ‑paris‑diderot.fr

Refere e1. Tomson, D. A. W. On Growth and Form 2nd edn (Cambridge

Univ. Press, 1942).2. Vogel, V. & Sheetz, M. Nature Rev. Mol. Cell Biol.7, 265–275 (2006).3. Lau enburger, D. A. & Horwitz, A. F. Cell 84, 359–369 (1996).4. Munevar, S., Wang, Y.-L. & Dembo, M. Biophys. J.

80, 1744–1757 (2001).5. Friedl, P., Heger eldt, Y. & usch, M.Int. J. Dev. Biol .

48, 441–449 (2004).

6. repat, X. et al. Nature Phys. 5, 426–430 (2009).7. Lecaudey, V. & Gilmour, D. Curr. Opin. Cell Biol.

18, 102–107 (2006).8. Poujade, M. et al. Proc. Natl Acad. Sci. USA

104, 15988–15993 (2007).9. Farooqui, R. & Fenteany, G. J. Cell. Sci.118, 51–63 (2005).10. De Rooij, J. et al. J. Cell Biol.171, 153–164 (2005).11. Saez, A.et al. Proc. Natl Acad. Sci. USA 104, 8281–8286 (2007).

T opological insulators are materialswith a bulk insulating gap, exhibitingquantum-Hall-like behaviour in the

absence o a magnetic eld. Such systemsare thought to provide an avenue or therealization o ault-tolerant quantumcomputing because they contain sur ace

states that are topologically protected againstscattering by time-reversal symmetry.However, topological phases in condensedmatter generally behave like ‘hothouse

owers’; they are beauti ul but ragile and,until now, were thought to be impossible tocreate without extremes o temperature and

magnetic eld. Tis conventional wisdommay be overturned by a pair o papers inthis issue1,2, which show that a certain classo three-dimensional topological insulatormaterial can have protected sur ace statesand display other topological behaviourpotentially up to room temperature without

TopoLogicaL insuLaToRs

The ext e er tSpin–orbit coupling in some materials leads to the formation of surface states that are topologically protected fromscattering. Theory and experiments have found an important new family of such materials.

J el M re

© 2009 Macmillan Publishers Limited. All rights reserved

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nature physics | VOL 5 | JUNE 2009 | www.nature.com/naturephysics 379

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E

E F

k x

ky

k x

ky

a b

F g 1 | ‘Light-like’ electrons, protected by time-reversal symmetry, in topological insulators. , A simplemodel of the surface band structure of a topological insulator with a single Dirac cone. We note thatthe Fermi level ( E F) does not, in general, pass through the Dirac point. b , A distinguishing feature of thetopological insulator surface is that there is a single electron spin state at each surface wavevector k, andthat states with opposite wavevector, –k, have opposite spin ‘orientation’.

magnetic elds. On page 398, Zahid Hasanand colleagues1 report the observation o characteristic signatures o a topologicalinsulator in the band structure o Bi 2Se3 studied using angle-resolved photoemissionspectroscopy (ARPES) and rst-principlescalculations. In contrast with previously studied materials, Bi 2Se3 is shown to havea large bandgap and a single sur ace Diraccone associated with the topologically protected state in the material. Concurrenttheoretical work using electronic structurecalculations, reported by Shou-Cheng Zhangand co-workers 2 on page 438, shows thatBi2Se3 is in act only one o an emerging classo new large-bandgap topological insulator,providing a simple tight-binding modelto capture their physical properties. Teseresults pave the way or the experimentalrealization and potential application o robust topological phases in a variety

o materials.What makes topological insulatorsdiferent rom ordinary band insulators?In a topological insulator, spin–orbitcoupling causes an insulating material toacquire protected edge or sur ace states thatare similar in nature to edge states in thequantum Hall efect. For example, the three-dimensional topological insulator phase 3,4 recently discovered in BiSb alloys5 hassur ace states that are predicted to remainmetallic even under quite strong disorder,as long as no magnetic elds or magneticimpurities break the time-reversal symmetry

that protects the phase. Such a sur acestate in a three-dimensional topologicalinsulator is a higher-dimensional analogueo one-dimensional current-carrying edgestates in the quantum spin Hall efect 6. In itssimplest orm, it can be viewed as a Dirac

ermion metal, similar to that in graphenebut without the two old valley and spindegeneracies (Fig. 1).

Although the phase observed in BiSballoys is theoretically the same as the onenow observed in Bi 2Se3, there are threecrucial diferences that suggest that Bi 2Se3 may become the re erence material or

uture experiments on this phase. First,access to the topologically protected sur acestate in BiSb is complicated by the presenceo several other sur ace bands. In contrast,ARPES measurements and theory show thatonly a single sur ace state is present in Bi2Se3,and that it has an electronic dispersionalmost the same as an idealized Dirac cone(Fig. 1). Second, Bi2Se3 is stoichiometric —it is a pure compound rather than an alloy like Bix Sb1−x — and, hence, can in principlebe prepared with higher purity and lessdisorder. Tis is important because althoughthe topological insulator phase is predictedto be quite robust to disorder, many

experimental probes o the phase, includingARPES measurements o the sur aceband structure, are clearer in high-purity samples. Tird, and perhaps most important

or applications, Bi2Se3 is ound to havea large bandgap, o approximately 0.3 eV(equivalent to 3,600 K), which agrees wellwith theoretical estimates o this quantity.

In combination with the absence o impurity states in the gap, this large bandgapindicates that topological insulator behaviourmay be seen at room temperature and greatly

increases the potential or applications. ounderstand the probable impact o thesenew materials, an analogy can be drawnwith the early days o high-temperaturesuperconductivity in the copper oxides: theoriginal cuprate superconductor, lanthanumbarium copper oxide, was quickly supersededby second-generation materials such asyttrium barium copper oxide and bismuthstrontium copper oxide or most scienti cand applications-related purposes. For three-dimensional topological insulators, Bi 2Se3 is likely to become part o such a second-generation class o material, superseding

the rst-generation BiSb. Another possiblesecond-generation topological insulatoris Bi2 e3. One o the topological insulatormaterials discussed by Zhang and colleagues 2,Bi2 e3 is already well known to materialsscientists working on thermoelectricity — itis a commonly used thermoelectric materialin the crucial engineering regime nearroom temperature.

Tis second generation o topologicalinsulators is likely to pave the way ora variety o experiments and potentialapplications. One class o proposedexperiment is based on the observation thata weak time-reversal-breaking perturbation

applied to a topological insulator opens asur ace bandgap. Tis results in a quantizedmagnetoelectric coupling (an appliedelectrical eld induces a magnetic dipoleand vice versa, with a proportionality constant o xed magnitude) resulting

rom a quantum Hall efect carried by thesur aces7. Although some efects resulting

rom this magnetoelectric coupling —labelled ‘axion electrodynamics’ becauseo an analogous interaction between theproposed axion particle and electromagnetic

elds — were discussed in the 1980s8

,it was then not clearly understood howsuch efects may be realized in realisticmaterials. Te improved understanding o magnetoelectric coupling that may result

rom experiments on topological insulatorsis also relevant to multi erroic materials,in which axion electrodynamics is a parto the ull magnetoelectric response9.Consequently, the observation o such aquantized magnetoelectric coupling in thetopological insulator is a high priority orexperiments, as this emergent property would complement the microscopic band

structure observed in photoemission1

.An even more ambitious experimentaldirection enabled by these new materialsis the study o how correlated-electronphysics such as superconductivity ismodi ed in a topological insulator. Oneparticularly intriguing example is theprospect o creating local Majorana ermionexcitations, which could be realized throughthe proximity efect between a topologicalinsulator and an ordinary ( ully gapped)superconductor 10. A de ning characteristico a Majorana ermion is that it is its ownantiparticle and there ore only has hal asmany degrees o reedom as a conventional




380 nature physics | VOL 5 | JUNE 2009 | www.nature.com/naturephysics

news & views

Hidden in the yellowing pages o century-old issues o Nature are some scienti cgems. They might be ully fedged ‘Lettersto the Editor’, curiosities rom ‘Notes’or nuggets rom ‘Our AstronomicalColumn’. Even the simple listings in‘Diary o Societies’, at the end o eachissue, can be ascinating — as is this entry(pictured) rom the issue o 17 June 1909.

At the behest o their boss,Ernest Ruther ord, at the University

o Manchester, Hans Geiger andErnest Marsden had been conductingexperiments on the scattering o α particles rom a thin gold oil. On that Junea ternoon — a century ago — they were topresent to London’s Royal Society their data“On the Di use Refection o the α Particles”(Proc. R. Soc. A 82, 495–500; 1909).

The rest really is history. Geiger andMarsden had observed that, althoughmost α particles passed throughthe oil pretty much undefected,very occasionally — and contrary toexpectation — an α particle could bescattered right back, through a very largeangle. Ruther ord had the interpretation:“the atom consists o a central chargesupposed concentrated at a point”, hewrote later ( Phil. Mag. 21, 669–688; 1911);the atom, ar rom being the ‘plumpudding’ that had been envisaged, hada nucleus.

Ruther ord acknowledged that theessence o his nuclear model had beencaptured in the ‘Saturnian atom’ oJapanese physicist Hantaro Nagaoka(Phil. Mag. 7, 445–455; 1904), “which hesupposed consisted o a central attracting

a fter ’ t

nucLEaR pHysics

mass surrounded by rings o rotatingelectrons”. But it was these data romGeiger and Marsden in 1909, and thosethat ollowed, that enabled the detail o thestructure o the atom to be drawn more

accurately than ever be ore. The nucleuswas revealed, and a century o nuclearphysics began.

aLison WRigHT

Dirac ermion such as the electron. So ar,Majorana ermions have not been observedclearly in experiment, but it has beenpredicted that in some situations an electronmay split into two Majorana ermions 10, andthat several interesting condensed-matterphases are believed to support them asemergent excitations. A direct observationo a Majorana ermion would be a key stepon the path to quantum computation usingtopological phases.

Tere are important open problems ortheory as well. Te topological insulatorphase can be de ned at the single-electronlevel, mani esting excitations having thequantum numbers (spin and charge) o the

electron, similar to the integer quantum Hallefect. In contrast, the ractional quantumHall efect is a topological phase displayingexcitations with ractional charges andstatistics. Our developing understanding o topological insulators may lead us to discovernew ‘ ractionalized’ phases o this sort. Tetwo papers in this issue demonstrate thatrapid experimental and theoretical progressin the research on topological insulators isboth answering and raising undamentalquestions pertaining to possible exotic phaseso electrons in solids. ❐

Joel Moore is in the Department of Physics,University of California, and the Materials Sciences

Division, Lawrence Berkeley National Laboratory,Berkeley, California 94720, USA.e‑mail: [email protected]

Refere e1. Xia, Y.-Q.et al. Nature Phys. 5, 398–402 (2009).2. Zhang, H. et al. Nature Phys. 5, 438–442 (2009).3. Fu, L., Kane, C. L. & Mele, E. J.Phys. Rev. Lett.

98, 106803 (2007).4. Moore, J. E. & Balents, L.Phys. Rev. B75, 121306 (2007).5. Hsieh, D. et al. Nature 452, 970–974 (2008).6. König, M. et al. Science 318, 766–770 (2007).7. Qi, X.-L., Hughes, . L. & Zhang, S.-C.Phys. Rev. B

78, 195424 (2008).8. Wilczek, F. Phys. Rev. Lett.58, 1799–1802 (1987).9. Essin, A. M., Moore, J. E. & Vanderbilt , D.Phys. Rev. Lett.

102, 146805 (2009).10. Fu, L. & Kane, C. L.Phys. Rev. Lett. 100, 096407 (2008).




joel moore- the next generation

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