It is the dream of physicists and electricalengineers alike to build electronic devicesthat can conduct electrical currents with

the minimal amount of resistance. Theminiaturization of electronics will soon leadto devices of the smallest possible physicaldimensions, in which quantum effectsbecome important. In this context, the ulti-mate conductor would be a very thin one-dimensional wire that has no defects toinhibit resistance-free currents. Electrons in such a wire are ballistic — that is, the wireis so clean that the distance travelled by the electrons between collisions is longerthan the wire itself. On page 51 of this issue de Picciotto et al.1 describe electricalconduction in a nearly perfect, ballistic one-dimensional wire. This groundbreak-ing work helps to establish fundamentallimits on the current-carrying capacity ofideal wires and their connections.

Imagine a perfect, extremely thin,straight wire in which electrons are allowedto move only along the wire. A perfect wirehas no defects, kinks or obstacles other thana connection at each end to allow current to pass through an external circuit, and per-haps two probes along the wire to measurethe voltage (Fig. 1a, overleaf). Will themotion of the electrons and hence conduc-tion of electricity in this wire proceed with-out resistance? De Picciotto et al.1 have cre-

ated this imaginary wire in the laboratory.They find that the resistance of a wire can beseparated into two parts: an ‘intrinsic resis-tance’ due to the scattering of electrons by imperfections in the wire, and a ‘contactresistance’ associated with the connectionsto the external circuit. The intrinsic resis-tance is measured by the two voltage probes,which draw negligible current. The authorsfind that in their defect-free wire the intrin-sic resistance does actually reach zero,although there is a finite contact resistanceof around 13 kV.

The vanishing of the intrinsic resistanceagrees with the simple notion that the cur-rent-carrying electrons should move freely if there are no obstacles. Our picture of elec-trical resistance as the result of momentum-changing deflections on charge-carriersdates back to the work of Drude around1900. The most effective deflections arethose that scatter charge-carriers in theopposite direction to that of their flow. Inthe late 1950s, Landauer2 became fascinatedwith the idea of electronic miniaturizationand proposed a conceptual framework forunderstanding electrical conduction inone-dimensional wires. Landauer realizedthat the wire can be thought of as being connected to electrochemical potentialreservoirs, in which many electrons of dif-ferent energies are available for conduction

(Fig. 1b). Once an electron enters the wire itcannot change energy, and only momentumchanges can affect the electrical current. Sowhere the wire is connected to the reservoirsthere is a mismatch of energies and a con-tact resistance develops. Conversely, in aregular three-dimensional wire, the contactresistance is very small and so tends to go unnoticed. But in a one-dimensional con-ductor, with no impurities, the intrinsicresistance must vanish although the con-tract resistance is high.

Until the 1980s most current measure-ments on mesoscopic devices (typically amicrometre or less in size) used a two-termi-nal geometry, in which voltage difference ismeasured solely between the current sourceand drain. But after Webb et al.3 developedthe technology to place multiple terminalson small metallic wires and rings, it was discovered that the four-terminal — twovoltage probes in addition to two currentleads — resistance of a non-ballistic wirechanges if the direction of an external magnetic field is reversed. This unexpectedresult was explained by Buttiker4, who generalized Landauer’s ideas to devices withmultiple terminals. He pointed out that, inthe absence of magnetic impurities, a four-terminal resistance should be unchanged by swapping over the current and voltageprobes and reversing the magnetic field.

After considering the multiple-terminalcase, Buttiker proposed that a two-terminalresistance must always contain a contactresistance, even if the wire is ballistic. Thiscontact resistance can be measured directlybetween point contacts that are shorter than the mean free path of electrons in anon-ballistic conductor5,6. Two-terminalmeasurements of ballistic wires also foundtheir resistance to be quite large, around 13kV. Is this resistance just the sum of the contact resistances?

De Picciotto et al.1 have built a multi-terminal one-dimensional conductor toaddress this issue. Classically a wire is con-sidered to be one-dimensional if its widthexactly accommodates the size of the chargecarriers with no room for wiggling. Elec-trons are essentially point objects, so this istechnically unfeasible. But this is wherequantum mechanics comes to the rescue. If an electron is made to occupy the lowestquantum-mechanical energy state in thelateral directions, without access to higherexcited states, it would be free to move onlyin one dimension. The key is to confineelectrons so tightly that the energy levels of the excited states are too high for them toreach. One way of doing this is to cool thewire to sufficiently low temperatures — butnot superconducting temperatures — so that the excited states are thermally inaccessible and conduction is strictly onedimensional.

To create the perfect one-dimensional

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NATURE | VOL 411 | 3 MAY 200 | www.nature.com 39

Fundamental physics

Resistance of a perfect wireAlbert M. Chang

Intuition tells us that a wire without defects should have zero resistance.But in the real world all conductors, however perfect, have someresistance. A new study confirms that electrical contacts are the problem.

from basalt depletion is offset by the posi-tive buoyancy that results from the lowertemperatures in the keel relative to those inthe surrounding, convecting mantle.

Lee et al.1 compare estimated variations inthe thickness, temperature and density of thelithospheric mantle with values calculated byassuming the isopycnic condition, and findthat the condition holds for the southwesternUnited States. So, if the lithospheric mantlewere to thicken further by conductive coolingin their study area, the deepest parts of themantle lithosphere would become less buoy-ant and sink into the convecting mantle — aslong as chemical depletion did not offset theincrease in negative thermal buoyancy. In this way, the degree of basalt depletionmodulates the thickness of the lithosphericmantle.

A further implication of the results1 is thatmore continental crust may have formedbefore 2.5 billion years ago than is indicatedby the present distribution of cratons. The

presence of thin Archaean lithospheric man-tle beneath the Basin and Range provinceraises the possibility that there could be similar lithospheric mantle under otherregions of the continents. We simply may nothave recognized it because Archaean litho-spheric mantle is commonly, but mistakenly,assumed to be thick and strong. Alternative-ly, the weakness of this thin lithosphere may have led to its preferential destructionthrough tectonic recycling. In either case,much more continental crust could haveformed in the Archaean than today’s distrib-ution of cratons would indicate. ■

Andrew A. Nyblade is in the Department ofGeosciences, Pennsylvania State University,University Park, Pennsylvania 16802, USA.e-mail: andy@geosc.psu.edu1. Lee, C.Y., Yin, Q., Rudnick, R. L. & Jacobsen, S. B. Nature 411,

69–73 (2001).

2. Jordan, T. H. J. Petrol. Special lithosphere issue 11–37

(1988).

3. Pollack, H. N. Earth Planet. Sci. Lett. 80, 175–182 (1986).

© 2001 Macmillan Magazines Ltd

wire, de Picciotto et al. use a precise semi-conductor growth technique called cleavededge overgrowth7 to grow alternate crys-talline layers of GaAs and AlGaAs in orthog-onal directions, which form a neat edge.Even more remarkably they have succeededin attaching non-invasive voltage probes tothe minuscule wire. The GaAs/AlGaAssheet forms a two-dimensional electrongas, and the authors place metallic elec-trodes on the surface to isolate the one-dimensional wire from the rest of the sheet(Fig. 1c). When negative voltages areapplied to these electrodes they deplete the two-dimensional electron gas beneaththem but preserve the one-dimensionalwire along the edge. The width of the metallic electrodes defines the length of theisolated wire. The separation between the electrodes also creates two narrow strips inthe two-dimensional electron gas that act asvoltage probes.

This set-up allows both four-terminaland two-terminal measurements to be madeon the same wire. In order to measure theintrinsic resistance, it is essential that thevoltage probes do not disturb the currentflow. With a one-dimensional wire this isusually impossible, but in their system dePicciotto et al. can tune the effect of the volt-age probe until it is almost non-existent.They show that whereas the intrinsic resis-

tance measured between the non-invasivevoltage probes vanishes, the two-terminalresistance of about 13 kV can be directlyattributed to the current contacts. This non-zero contact resistance indicates that there is a minimum resistance for the passage ofelectricity regardless of how perfect a wiremay be.

It would be interesting to explore thepossibility of circumventing the limitationsimposed by the presence of contact resis-tances. One can imagine measuring the electrical properties of one-dimensionalconductors using a contact-free method,such as capacitance coupling, to inducecharge motion. The results of studies likethat of de Picciotto and colleagues will applyequally to carbon nanotubes and other one-dimensional systems, and will becomeincreasingly important as electronics getsever smaller. ■

Albert M. Chang is in the Department of Physics,Purdue University, West Lafayette, Indiana 47907-1396, USA.e-mail: yingshe@physics.purdue.edu1. de Picciotto, R., Stormer, H. L., Pfeiffer, L. N., Baldwin, K. W. &

West, K. W. Nature 411, 51–54 (2001).

2. Landauer, R. IBM J. Res. Dev. 1, 223–231 (1957).

3. Webb, R. A., Washburn, S., Umbach, C. P. & Laibowitz, R. B.

Phys. Rev. Lett. 54, 2696–2699 (1985).

4. Buttiker, M. Phys. Rev. Lett. 57, 1761–1764 (1986).

5. van Wees, B. J. et al. Phys. Rev. Lett. 60, 848–850 (1988).

6. Wharam, D. A. et al. J. Phys. C 21, L209–L214 (1988).

7. Pfeiffer, L. N. et al. Appl. Phys. Lett. 56, 1697–1699 (1990).

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40 NATURE | VOL 411 | 3 MAY 2001 | www.nature.com

Daedalus

Scroll-readingThe ancient world guards its secrets well.In the buried ruins of Herculaneum, themany scrolls that make up the library ofPhilodemus wait to be deciphered. Sadly,the scrolls have been carbonized, and it is extremely difficult to unwind them for normal reading. Daedalus now has an idea.

The nuclear magnetic resonanceimager should make it possible to scansuch scrolls without unrolling them.Interpreting a scrolled image would takevery clever software, but it seems feasible.More problematically, could the bestmodern machines resolve the lettering?Fortunately, the basic pixel of a coil iscurved, like that of a scroll, and alsoextends in depth, again like a scroll. Withluck, a scroll rotated in a superconductingcoil, and slowly moved in and out of it,should yield up its lettering to acontrolling scholar.

Of course, nobody believes in theWisdom of the Ancients any more. Nomatter what amazing statements or beliefsare found in antique libraries, letter filesor rubbish dumps, the job of scholars willbe to decipher, translate and interpret.Simple letters inviting somebody to aparty, or denying an allegation, may behandled most easily; documents claimingto be part of a revelation will give a lotmore trouble.

The basic problem, however, is whatnucleus to look for in the magnetic-resonance output. Ancient inks were based on soot (carbon), which might have little contrast with the surroundingcarbonaceous papyrus or vellum, unless it contains germanium or potassium, from coal or wood. It might be better toexamine the vehicle (gum), which wouldhave more hydrogen, and more mobilehydrogen, than the lettering itself. If so,preliminary steaming of the scroll couldhelp. If any of the inks were based on black iron gallate, the signal fromparamagnetic iron should be easy todetect. Either way, Daedalus reckons thatsome sort of contrast change between inkand background could be detected by theinstrument and highlighted by itssoftware, enabling a scholar to read theentire scroll without the pain ofunwinding it.

Even the problem of dating the findmay become tractable, if the changes in theink, vehicle and substrate turn out to befairly predictable in time. And if in thefuture a better method becomes available,why, the scroll is still there, undamaged byclumsy attempts to unroll it. David Jones

Figure 1 Measuring resistance in one-dimensional wires. a, An ideal one-dimensional conductor with two currentterminals and two voltage probes, whichdraw no current. The two terminalresistance, R2p, is defined as (Vs1Vd)/I,whereas the four-terminal intrinsicresistance, Rint, is given by (Vp21Vp1)/I. b, Landauer’s concept2 of a perfect one-dimensional wire, in which electronreservoirs with unbalancedelectrochemical potentials (m4m s1md)provide current source and drain. Notethat m4 1eV, where m is theelectrochemical potential, e is thefundamental electric charge and V is thevoltage. The measured resistances dependon the transmission and reflectionprobabilities of the electrons within theconductor. In particular, for a four-terminal intrinsic resistance to be zero,the transmission and reflectionprobabilities from the left and rightreservoirs into a voltage probe must benearly equal (Tsp14Tdp1). This is onlypossible if the conductor is ballistic anddevoid of obstacles. c, The perfect one-dimensional wire created by de Picciottoet al.1 with two current and two voltageterminals created from the same two-dimensional electron gas.

Metallicgates

1-D wire

Currentdrain

Currentsource

Voltageprobe 1 Voltage

probe 2

2-Delectrongas

Vp1 Vp 2

Current I

I

I

Currentdrain

Leftreservoir

Rightreservoir

Currentsource

Ballisticelectron

Vd Vs

µd =-eVd

µp1=-eVp1 µp1=-eVp2

µs =-eVs

Tsp1Td p1

a

b

c

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