as rapidly as other cities including Mumbai(India), Dhaka (Bangladesh) and Lagos(Nigeria) (Fig. 2). Full implementation of thePAHO strategy is needed in the megacitiesand the surrounding regions to stop measlestransmission. If this proves to be impossible,new approaches such as development of newvaccines for administration in early infancymay be needed.

Grenfell and colleagues2 show that, in thepre-vaccine era, waves of measles infectionmoved away from London at a speed ofaround 5 km per week and were evident up to30 km away from the city. There was a timelag between the peak in the originatingurban centre and its arrival in the periphery— the lag was greater for smaller and moredistant towns. Given this pattern, it is tempting to think that the extent of measles outbreaks can be controlled by vaccinationahead of the epidemic. But attempts to control outbreaks show that once a wave ofinfection has been established, it is difficultto stop it through selective vaccination.Often the intervention comes too late or, if it is in time, the ‘wave’ of measles infectionstill sweeps over and around the ‘breakwater’.Current recommendations are that measlesoutbreaks should be prevented rather thancontrolled after they have started8. But vacci-nation in areas next to districts in which anoutbreak occurs may be effective if high coverage of all susceptible age groups isachieved.

From Grenfell and colleagues’ results, itmight seem that concentrating on citieswould be an effective vaccination strategy(although this is not something they them-selves propose). This approach — based onthe idea that cities are the key disease reser-voirs — has been tried in Africa, and has notworked. In the late 1990s, Burkina Faso andMozambique conducted mass vaccinationcampaigns, targeting children of preschoolage in the largest cities with the aim of pre-venting spread to more remote rural townsand villages that health services found hardto reach. In both countries, the urban cam-paigns were associated with some reductionin the size of the expected epidemic in the citybut were unsuccessful in preventing diseasespread to rural areas9. The urban campaignsstill left enough susceptible city dwellers to result in an epidemic, and then humanmigration seeded the periphery, leading tolarge outbreaks elsewhere.

These examples reinforce the need foruniversal vaccination against measles for allchildren regardless of where they live. Thesheer number of people moving around forbusiness or pleasure, in addition to forcedmigrations, make importation of measles a common occurrence: achieving and maintaining high population immunity byvaccination throughout an entire country is the only proven way of preventing largeoutbreaks.

The results in Grenfell et al.’s paper shouldstimulate activity in at least two areas. First, itis likely that the city-to-village dynamics thatthey document for measles also apply toother common human diseases. Amongthem are some that can be prevented by vac-cines (rubella, mumps, varicella and hepatitisA) and some that, as yet, can’t (those causedby respiratory syncitial virus, rotaviruses andadenoviruses), and influenza, which has pan-demic potential but is vaccine-preventable.Better characterization of the patterns of disease transmission in space and time couldoffer unique opportunities for prevention: in particular, more research is needed on theeffect of long-range jumps of infection thatoccur, for example, with air travel.

Second, the new work highlights thevalue of careful collection, analysis, dissemi-nation and storage of disease-surveillanceinformation. Accurate records of measlescases were kept in England and Wales longbefore vaccination against the disease wasintroduced, and Grenfell and colleagues’sophisticated time-series analyses were possible only because of the geographicallydetailed and complete nature of the data sets.We would be wise to strengthen the disease-

surveillance systems in both developed anddeveloping countries, and to include collec-tion and storage of clinical specimens as partof that endeavour. Not only is such informa-tion essential for immediate disease control,but it will also make possible future researchwith analytical or laboratory methods yet tobe devised. ■

Peter M. Strebel and Stephen L. Cochi are at theNational Immunization Program, Centers forDisease Control and Prevention, Atlanta, Georgia30333, USA.e-mail: pstrebel@cdc.gov1. Anderson, R. M. & May, R. M. Nature 318, 323–329 (1985).

2. Grenfell, B. T., Bjørnstad, O. N. & Kappey, J. Nature

414, 716–723 (2001).

3. de Quadros, C. A. et al. J. Am. Med. Assoc. 275, 224–229 (1996).

4. Hersh, B. S., Tambini, G., Nogueira, A. C., Carrasco, P. &

de Quadros, C. A. Lancet 355, 1943–1948 (2000).

5. World Health Organization Weekly Epidemiol. Rec.

74, 429–434 (1999).

6. Gay, N. et al. Commun. Dis. Rep. CDR Rev. 7, R17–R21 (1997).

7. Orenstein, W. A. et al. Am. J. Pub. Health 90, 1521–1525 (2000).

8. Aylward, R. B., Clements, J. & Olive, J. M. Int. J. Epidemiol.

26, 662–669 (1997).

9. WHO Intercountry Office for Eastern Africa. Summary of

presentations, reports and recommendations of the East Africa

measles strategy clarification meeting. Nairobi, Kenya. World

Health Organization, 11–13 October, 1999.

10.http://www-nt.who.int/vaccines/globalsummary/timeseries/

tsincidencemea.htm

11.http://www.unpf.org/swp/2001/english/tables.html

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696 NATURE | VOL 414 | 13 DECEMBER 2001 | www.nature.com

Copper oxide compounds are note-worthy for the relatively high tempera-tures (up to 160 K) at which they lose

their resistance to electrical currents andbecome superconducting. This was discov-ered by Bednorz and Müller1 in 1986, andgave birth to the field of ‘high-temperature’superconductivity. High temperatures aside,the unconventional nature of the super-conducting mechanism in these materialshas puzzled researchers ever since.

In 1986, few would have guessed that ashock wave produced by that scientific earth-quake would reach an old realm of solid-statephysics 15 years later and shake one of its mostfundamental concepts. But on page 711 of thisissue, Hill et al.2 report that, at low tempera-tures (close to absolute zero, or 1273 °C), a copper oxide material in which the super-conducting state has been suppressed violatesthe Wiedemann–Franz law. This universallaw relates two basic properties: the ease withwhich a solid conducts heat and charge. Asthis is the first time a material has been foundthat deviates from this law, it reveals, yetagain, that high-temperature superconduc-tors are far from being understood.

Almost 150 years ago, Wiedemann andFranz discovered a remarkable correlationbetween the thermal and electrical conduc-tivities of various metals — good conductorsof electricity are also efficient conductors of heat. At room temperature the ratio of the two conductivities was found to be very similar for a broad range of metals. Severaldecades and a scientific revolution later, this ratio was linked to two fundamentalconstants: the quantum of electrical charge,e, and the ‘quantum’ of entropy, kB (betterknown as the Boltzmann constant). Roughlyspeaking, entropy measures the disorder of electrons and is the microscopic origin of ‘heat’.

The fundamental mechanism behind theWiedemann–Franz correlation is easilygrasped. The propagation of electrons in acrystal is impeded by the presence of anyimperfection (impurities or defects). Sothere is always a maximum finite distancethat an electron can travel before being scat-tered. Because the electron carries both heatand charge, scattering will affect thermal andelectrical conductivities in the same way.This is strictly true only if the scattering is

High-temperature superconductivity

Charged with smuggling heatKamran Behnia

Good conductors of heat are usually good at conducting electricity. So thediscovery that electrons in a superconductor can carry an unauthorizedamount of heat at low temperatures raises many questions.

© 2001 Macmillan Magazines Ltd

‘elastic’ — that is, when the collision is notassociated with any change in the particle’senergy. This means the Wiedemann–Franzlaw should always hold true at a temperatureof absolute zero when all scattering becomeselastic. As the temperature tends to zero, theratio of thermal conductivity to electricalconductivity divided by temperature tendsto a constant value. This statement is true forall metals tested to date.

The twentieth century saw the develop-ment of the ‘band structure’ theory of electronbehaviour in solids, which treats electrons as individual free entities. Surprisingly, thistheory — which ignores the strong electro-static repulsion between the electrons — has been successful in describing the mainelectronic properties of various metals. In1956, Lev Landau revealed the reason behindits success. He formulated the concept of a ‘Fermi liquid’, in which the interacting electrons are replaced by ‘quasiparticles’ thatinteract but can still be treated as particles (inthis case, fermions) with the same spin andcharge as a free electron. The only differencebetween quasiparticles and electrons is thatthe quasiparticle has a modified mass, whichreflects the size of the electronic interactions.

It is hard to exaggerate the fecundityof Landau’s theory. Most metallic elementsand compounds are Fermi liquids. There areeven exotic metals — in which strong inter-actions between electrons create Landauquasiparticles several hundred times heavierthan a free electron — that fit within theband-structure theory. But do other types of strongly interacting electronic systemsexist? In other words, are Fermi liquids onlyone of many correlated-electron systemsfound in nature? This question has beenhaunting condensed-matter physicists forthe past 30 years.

The copper oxides challenged the Fermi-liquid picture almost as soon as they were discovered. And we are still far from under-standing the elementary excitations (akin to quasiparticles) found in the metallic (‘normal’) state of these compounds. Thesesuperconductors have unusual origins. Theparent compound is a Mott insulator, whichshould be a conductor according to the standard band-structure theory, but fails toconduct because of strong repulsive inter-actions between the electrons. A metallicstate can be created in a Mott insulator byinjecting it with conducting electrons — forexample, by altering its chemical structure(chemical doping). This is how a copperoxide insulator is turned into a copper oxidesuperconductor.

But the Fermi-liquid picture cannot easily explain the metallic state of a dopedMott insulator. For example, angle-resolvedphotoemission data indicate that Landauquasiparticles appear only in the supercon-ducting state3. These and other experimentalfindings have led to alternative descriptions

of the elementary excitations in these sys-tems. One recurrent feature of these ‘non-Fermi-liquid’ theories is the separation oftwo of the most fundamental properties ofan electron: its ‘spin’ and its charge. In thewords of P. W. Anderson, “the electron falls apart” in such a way that different excita-tions are responsible for carrying its spin and charge. But this idea has been difficult to check experimentally because there is noestablished method for directly probingtransportation of the electron spin.

Hill and colleagues2 approach this mys-tery from a new angle. They investigate thetransport of heat in the normal metallic stateof a copper oxide superconductor at milli-kelvin temperatures. In all superconduc-tors, whether low- or high-temperature, thezero-resistance state can be destroyed byapplying a high enough magnetic field (thesize of the field is determined by the super-conducting transition temperature). Thecopper oxides usually require fields that aretoo high to achieve experimentally, but thecompound studied by Hill et al. has a transi-tion temperature of just 20 K, so super-conductivity can be removed by applying a much smaller magnetic field. Hill et al.measure the thermal and electrical conduc-tivity of the ‘normal’ state of their compound(at low temperatures and under appliedfields), and discover a clear departure fromthe Wiedemann–Franz law. They show thatthere is no correlation between thermal and electrical conductivity at very low tem-perature. Instead, the heat conductivity isconsistently greater, although the excess suddenly vanishes below 0.3 K. Because theWiedemann–Franz law is a natural conse-quence of the Fermi-liquid picture, thisspectacular violation has immediate conse-quences for understanding the elementaryexcitations in copper oxides. Taken at its facevalue, it means that charge and heat are notcarried by the same type of electronic excita-tions, so there may indeed be some sort ofspin–charge separation in these materials.

This is really just the beginning. We needto repeat the measurement on superconduc-tors with different amounts of chemical doping to determine exactly when theFermi-liquid picture breaks down. More-over, studies of other compounds at highermagnetic fields may indicate whether theexcess heat flow is associated with electronspin, as suspected. Most pieces of this hugepuzzle of modern condensed-matter physicsare still waiting to be put into place. ■

Kamran Behnia is in the Laboratoire de PhysiqueQuantique, Ecole Supérieure de Physique et deChimie Industrielles, 10 rue Vauquelin, 75005 Paris,France.e-mail: kamran.behnia@espci.fr1. Bednorz , J. G. & Müller, K. A. Z. Phys. B 64, 189–193

(1986).

2. Hill, R. W., Proust, C., Taillefer, L., Fournier, P. & Greene, R. L.

Nature 414, 711–715 (2001).

3. Kaminsky, A. et al. Phys. Rev. Lett. 84, 1788–1791 (2000).

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NATURE | VOL 414 | 13 DECEMBER 2001 | www.nature.com 697

100 YEARS AGOThe practicability of effecting the purificationof town sewage on the large scale bybacterial agency has now been abundantlyproved. The process has passed beyond theexperimental stage, and must now beacknowledged as the only method which canconvert the putrescible matter of sewage onthe large scale into inoffensive and harmlesssubstances. Accordingly all trustworthyinformation respecting the results whichhave been arrived at from the lengthyexperimental trials, and from the applicationof these results on the large scale, will bewelcome to public sanitary authorities, andperhaps even still more acceptable to theprofessional advisers of these bodies. Thetreatise under review has been written byone who has carefully watched the progress,and who has had a long and variedexperience, of bacterial treatment. The bookis, therefore, undoubtedly worthy of carefulperusal and consideration by those who areresponsible for disposing of the sewage fromhouses, villages or towns.From Nature 12 December 1901.

50 YEARS AGOTeletherapy units using radium are limited inusefulness by the low radiation intensitiesproduced by the small amounts of radiumwhich can be used. To secure an adequatedosage-rate, the distance between thesource and the tumour cannot be more thana few centimetres, and therefore the dosedelivered to the skin lying between thesource and the tumour is much higher thanthat delivered to the tumour. The dose-ratebelow the surface, expressed as apercentage of the dose-rate at the skin,decreases very rapidly with increasing depth.Thus the percentage depth-dose isinfluenced primarily by the inverse squarelaw, and one of the chief advantages of high-energy radiation, namely, its smallattenuation by the tissue between the sourceand the tumour, is not realized. Any attemptto obtain an improvement in the depth-doseby increasing the amount of radium, andcorrespondingly improving the ratio betweenthe source-to-tumour distance and thesource-to-skin distance, is limited by thehigh cost of radium, and by the requiredincrease in the volume of the source. If thediameter of the source is increased, it isharder to get a well-defined beam; if thethickness in increased, much of the radiationis lost by absorption within the source.From Nature 15 December 1951.

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