The heyday of research into the basic properties of in-termetallic superconductors took place between 1950

and 1980. During those years, the number of known su-perconducting intermetallic compounds (consisting of sev-eral metallic and metalloid elements) grew explosively,and superconducting transition temperatures Tc werepushed to just over 23 K (Nb3Ge). (In comparison, the firstsuperconductor, discovered by Heike Kamerlingh Onnes in1911, was mercury, with Tc = 4.15 K). Research groups allover the world searched for higher and higher Tc values.The researchers were motivated by a basic desire to findan intrinsic limiting temperature for this intriguing quan-tum phase and by a very applied interest in making use-ful superconducting devices.

By the 1970s, an empirical glass ceiling seemed tohave been hit. Transition temperatures were stuck at 23K, and some theorists proclaimed that higher transitiontemperatures were not possible. The basic research com-munity became more interested in other issues in super-conductivity, such as the interaction of local magnetic moments with superconductivity, heavy-fermion super-conductors, organic superconductors, and, more recently,the high-temperature, copper oxide–based ceramic super-conductors. With the discovery of high-Tc superconductiv-ity over a decade ago, the 23-K ceiling for Tc was shat-tered, giving us not only new horizons in transitiontemperature (the current record is about 160 K underpressure) but also a profusion of interesting phenomenalike d-wave pairing symmetry, pseudogaps, stripes, andexotic pairing mechanisms. Conventional wisdom holdsthat these new horizons are enabled by the complexity ofmultielement compounds. These complex materials, inturn, have required complex processing to achieve the in-dustrial production of superconducting wires and devicesthat is now taking place.

The January 2001 discovery that magnesium diboridebecomes superconducting at about 40 K produced an ex-plosion of enthusiasm and excitement. Although 40 K isindeed much cooler than 160 K, it represents a near dou-bling of the previous record intermetallic Tc and meansthat MgB2 can be cooled to an operational temperature byeither liquid hydrogen or readily available, fairly inex-pensive, closed-cycle refrigerators. In addition, MgB2 is a

simple compound of two abundant, in-expensive elements. The long sought-after, high-temperature, intermetallicsuperconductor had finally made itsappearance—better late than never.

Although the initial interest inMgB2 arose solely from its high Tc, fur-ther work revealed that MgB2 breaks

new ground for superconductivity based on the well-knownelectron–phonon interaction. The material displays aplethora of remarkable features. MgB2 not only has im-portant technological potential (figure 1 and the cover ofthis issue show images of MgB2 wire), but also will have alasting impact on how the research community looks atand looks for superconductors.

The understanding of this material has grown at awhirlwind rate, driven by the immediacy of preprint post-ings on the Internet. The daily appearance of new researchresults brought theory and experiment into resonance anddramatically accelerated progress in the internationalcommunity. Thanks to that positive feedback, the basicphysical properties of MgB2 were delineated within a yearand a half of its discovery.1

Background and foreshadowingFor decades after the discovery of superconductivity, theexperimental data puzzled theorists. One of the key ex-periments that pointed toward the correct approach to un-derstanding the phenomenon was the isotope effect, whichshowed that the transition temperature depends on themass of the superconducting atoms. Motivated in part bythose experiments, theorists recognized that lattice vi-brations (phonons) could produce an attractive interactionbetween the like-charged electrons. The 1957 theory ofJohn Bardeen, Leon Cooper, and J. Robert Schrieffer(BCS) explained superconducting properties quantita-tively using an elegant microscopic theory and the elec-tron–phonon interaction as the mechanism for pairingelectrons.

At the most basic level, the superconducting groundstate is a coherent superposition of Cooper pairs—pairs ofelectrons coupled by an attractive force. The attraction canarise from phonons in the following way. As a negativelycharged electron moves through a lattice of positive ions,it attracts and locally distorts the lattice in its neighbor-hood. The residual distortion left in its wake produces anet positive charge that attracts a second electron.

The key feature of the superconducting state is the en-ergy gap in the excitation spectrum. Below Tc, this gap pre-vents scattering of the electrons and produces zero elec-trical resistance. The gap also manifests itself in tunnelingexperiments (in a manner similar to a semiconducting gap)that map its energy dependence and in thermodynamic ex-periments, such as specific heat measurements, that probethermal excitations across the gap.

One of the most significant and influential predictionsof the BCS theory is the description of Tc in terms of twofundamental constants (Boltzmann’s constant kB and

34 March 2003 Physics Today © 2003 American Institute of Physics, S-0031-9228-0303-010-2

Paul Canfield is a senior physicist at Ames Laboratory and aprofessor in the department of physics and astronomy at IowaState University in Ames, Iowa. George Crabtree is a senior scientist and the director of the materials science division at Argonne National Laboratory in Argonne, Illinois.

With a superconducting transition temperature of 40 K andtwo superconducting gaps, MgB2 is full of surprises for bothexperimentalists and theorists.

Paul C. Canfield and George W. Crabtree

Magnesium Diboride: Better Latethan Never

Planck’s constant \) and three basic materials parameters:

kB Tc = 1.13 \wD exp[–1/VN(EF)].

The Debye frequency wD is the characteristic frequency ofthe acoustic lattice vibrations. It sets the energy scale ofthe attractive interaction between Cooper pairs. In thesimplest model of a solid, the atoms can be viewed asmasses m connected by springs with spring constant k.From high-school physics (or what should be high-schoolphysics), the characteristic frequency of such an idealizedmodel is w = (k/m)1/2. This simple observation, combinedwith the BCS formula above, is the essence of the isotopeeffect. Within this framework, Tc is inversely proportionalto the square root of the masses of the constituent ele-ments. So, to first order, compounds with lighter elementshave a better shot at higher values of Tc.

The electron–electron attractive interaction V is acaliper of the strength of the electron–phonon interaction.If the electron–phonon interaction is increased, V and Tcrise, but if it becomes too large, it can induce a phase tran-sition to a different structure, often with vastly inferior su-perconducting properties. For that reason, researchershave often sought high values of Tc near, but just short of,structural phase transitions; that approach is the mostpragmatic method of maximizing V for a given structure.

The density of itinerant electron states N(EF), whereEF is the Fermi energy, provides a caliper of the number ofelectrons that can participate in the superconductingstate. The larger N(EF), the larger Tc. Given that transi-tion metals with partially occupied d shells tend to havelarge values of N(EF), conventional wisdom held that highvalues of Tc could be found in transition-metal compounds.

Experimentally, it is possible to tune N(EF) by varyingthe chemical composition in an isostructural series of com-pounds. Using light elements can raise wD. Experimental

searches for new superconductors often placed a muchlarger emphasis on N(EF) and wD than on V, because theelectron–phonon coupling—and hence V—is hard to pre-dict or control.

MgB2: Discovery and isotope effectBased on these experiments, theories, and prejudices,groups around the world searched for ternary or quater-nary compounds that were rich in light elements such aslithium, boron, carbon, and magnesium. Jun Akimitsu’sgroup at Aoyama Gakuin University in Japan explored thetitanium-boron-magnesium ternary phase diagram. Thatsystem has two light elements as well as the transitionmetal Ti, which could provide 3d electrons to boost N(EF).Two years ago,2 the researchers indeed found a remark-ably high Tc, but in a simple binary compound: MgB2 en-tered the superconducting state just below 40 K (see fig-ure 2). In early January 2001, Akimitsu reported theirresults at a meeting in Sendai, Japan. His announcementset off a rush of experimental and theoretical work to con-firm and explore that remarkably high transition temper-ature in a binary intermetallic compound (see PHYSICSTODAY, April 2001, page 17).

Whereas MgB2 is a simple binary compound (only threeatoms per hexagonal unit cell), it is hard to make by con-ventional methods. For starters, elemental Mg has a highvapor pressure. Furthermore, MgB2 decomposes ratherthan melts and does not have any accessible liquid–solidtransitions at ambient pressures.1,3 Simple crystal growthof MgB2 thus appears to be intractable. (This difficulty isone of the reasons that superconductivity in MgB2 was notdiscovered 40 years ago.) Fortunately, MgB2 can be synthe-sized by a simple, alternate route: reaction of B (in any num-ber of forms) with Mg vapor, generally at a temperature ofabout 900°C for as little as a couple of hours. To date, this

http://www.physicstoday.org March 2003 Physics Today 35

Figure 1. Magnesiumdiboride was discov-ered in 2001 to be-come superconduct-ing below about40 K, a remarkablyhigh transition tem-perature for an inter-metallic compound.This image from anoptical microscopeshows a cross sec-tion of a MgB2 wire,about 150 mm in di-ameter, composed offine grains with awide distribution oforientations. (Fromref. 4.)

method has been used to form MgB2powder, sintered pellets, wires, andfilms.1,3–5 The wires shown in figure1 and on the cover of this issue weremade from B filaments using thistechnique. More recently, high-pressure, high-temperature meth-ods of growing MgB2 have been de-veloped, and single crystals withmasses approaching a milligramare becoming available.1,6

By exposing isotopically pure 11Bor 10B powder to Mg vapor, sintered pellets of Mg11B2 andMg10B2 are simple to synthesize. The first measurements1,3

of the isotope effect revealed the importance of the elec-tron–phonon interaction for the Cooper pairing mechanismin MgB2: Tc shifted by 1.0 K when 11B was substituted for10B, as shown in the figure 2 insets. The isotope shift asso-ciated with Mg can be measured, too. Surprisingly, substi-tution of 24Mg for 25Mg produced almost no shift in Tc.1,7 Thecontrast of these two results is striking and immediately in-dicates a highly selective electron–phonon interaction. Amore subtle experimental effect was also found: The totalisotope shift for Mg plus B is significantly smaller than thatpredicted by the BCS theory.1,7 The origin of the discrepancycannot be inferred from the experiment. It turns out to bedue to another unique feature of MgB2: the nature and ex-treme strength of the electron–phonon coupling responsiblefor superconductivity in this compound.1,8

If MgB2 is an electron–phonon superconductor, how canit have such a high Tc? From the BCS formula, Tc dependson only three materials parameters: the characteristicphonon energy \wD, the electronic density of states N(EF),and the electron–phonon interaction giving rise to V. Thephonon energies of MgB2 are indeed rather high, but not es-pecially different from other diborides and light-element bi-nary compounds that have much lower values of Tc. Thedensity of states is low—MgB2 has no d electrons. The BCSformula leaves only one other source for high Tc: the elec-tron–phonon coupling as expressed through V. This simpleanalysis turns out to be prescient: The selective coupling be-tween specific electronic states and specific phonons is thekey feature that drives superconductivity and other inter-esting properties of this compound.

All bands are not created equalMagnesium diboride has a simple crystal structure con-sisting of hexagonal Mg layers alternating with honey-comb B layers, as shown in figure 3a. The Mg ions donateelectrons to the conduction bands, but the Mg atomic or-bitals play only a small role in the conduction process—it’sthe honeycomb planes of B that determine the electronicproperties.1,8

The B electronic states can be best understood by re-calling the benzene molecule from high-school chemistry (orwhat should be high-school chemistry). In benzene, the sp2

carbon orbitals overlap, creating s bonds between neigh-boring atoms in the plane of the molecule. The remainingcarbon p orbitals extend above and below the plane and cre-ate the p bonds. The electrons in both bonds are delocalizedamong the six C atoms in the benzene ring, although theymay not jump from the s to the p bonds. In MgB2 , the Bhoneycomb plays the role of the C ring in benzene, with thekey differences that the rings form an extended two-di-mensional network and electrons are delocalized through-out the honeycomb. The s and p bonds in benzene becomes and p bands in MgB2, with very little electron hopping be-tween them. In MgB2, the p bands connect adjacent B lay-ers (through the inert Mg ions), which allows metallic con-duction perpendicular to the B sheets (conventionally calledthe c-direction) as well as parallel to the B sheets. The selectrons are restricted to the B layer and conduct only inthis basal plane. The geometry of the electron densities as-sociated with these bands is depicted in figure 3b. The bandstructure can be represented compactly in momentum spaceby its Fermi surface, the energy contour separating filledfrom empty electronic states, shown in figure 3c.

These two nearly noninteracting bands of different di-mensionality are key ingredients in MgB2. The other keyingredient is the bands’ special sensitivity to phonons. Inconventional superconductors, the electron–phonon inter-action creates Cooper pairs of approximately equal pair-ing strength, distributed evenly over the Fermi surface. InMgB2, there is one high-energy (about 570 meV) opticalphonon (denoted E2g for its symmetry), associated with thein-plane motion of the B atoms, that couples very stronglyto electrons in the 2D s band. The strong coupling of theB motion to the s states originates in the special covalentnature of the s band. Unlike conventional metallic bands,the s band has charge concentrated along the B–B axes(see figure 3b) rather than spread throughout the unit cell.Thus, when the B atoms move in the plane, the chargemust redistribute significantly to accommodate the

36 March 2003 Physics Today http://www.physicstoday.org

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Figure 2. Magnesium diboride’s superconducting transition below

about 40 K is clearly seen in the tem-perature dependence of the electrical

resistivity r. The insets show the effect of replacing boron-10 with

boron-11: a reduction of about 1 K in the transition temperature. The isotope effect is seen in transport

properties, such as normalized tem-perature-dependent resistivity in thetop left plot, and in bulk thermody-

namic properties, such as the normalized magnetization M

plotted in the lower right.

change, and the golden hexagonal network of charge in fig-ure 3b becomes substantially distorted. The distortionshifts the energy of the electronic states and accounts forthe large coupling energy. This picture of two bands of different dimensionality with strong selective electron–phonon coupling is confirmed by detailed measurementsof the electronic structure, such as experiments that usequantum oscillations of the magnetization (the deHaas–van Alphen effect) to infer the local Fermi surfacegeometry and the electron density of states.1,9

The E2g phonon has a large impact on the propertiesof MgB2 because it affects the conduction electrons; had itcoupled to the fully filled or empty bands, the conse-quences would be far less dramatic. Physically, this domi-nant phonon mode sets the energy scale for the supercon-ductivity and its characteristic energy replaces \wD as theprefactor in the BCS equation for Tc (roughly a factor of 10enhancement!). In addition, the highly selective elec-tron–phonon interaction gives rise to the substantialboron—and negligible magnesium—isotope shift. It alsoanswers the question of how Tc is so high, given the rela-tively low N(EF).1,10

Basic propertiesHow do the special features of the band structure and elec-

tron–phonon interaction in MgB2 manifest themselves? Al-most every possible measurement shows their effect. Eventhe normal-state resistivity shown in figure 2 is curious inits own right.1,4 One of the old rules of thumb for inter-metallic superconductors was that a high Tc is associatedwith large room-temperature resistivity arising from thestrong electron–phonon scattering of electrons in the nor-mal state. Magnesium diboride, though, has a low room-temperature resistivity (about 10 mW cm) and a very lowresistivity just above Tc (around 0.5 mW cm). Its resistivityis thus comparable to bulk copper wire. In contrast, the su-perconductor Nb3Sn has a resistivity of 80 mW cm at roomtemperature and 10 mW cm just above its Tc. The low re-sistivity of MgB2 is simply a consequence of having twobands with very different electron–phonon couplingstrengths. In essence, the two bands take turns shortingeach other out. (To understand such behavior qualitatively,look at figure 3b and think of the contours as forming par-allel networks of resistors.) The high-temperature resis-tivity is dominated by the 3D p band, which has thesmaller electron–phonon coupling, whereas the supercon-ductivity is primarily due to the larger coupling in the 2Ds band. This simple picture implies a moderate anisotropyin the normal-state resistivity, with a larger resistivity inthe c-direction than in the basal plane; such anisotropy hasindeed been observed.1

Another startling aspect of MgB2 is the anisotropy ofits upper critical magnetic field Hc2. The upper critical fieldis the highest magnetic field (at a given temperature) forwhich a material will remain a bulk superconductor. Themagnetic field strength needed to destroy superconductiv-ity in bulk MgB2 depends on the orientation of the fieldwith respect to the crystal axes, as shown in figure 4.

http://www.physicstoday.org March 2003 Physics Today 37

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Figure 3. Structure of magnesium diboride. (a) The crystal structure of MgB2 features hexagonal planes of magnesium (yel-low) interleaved with honeycomb layers of boron (blue). (b) The boron atoms form a two-dimensional network of s bondsand a three-dimensional network of p bonds; the two networks yield corresponding bands of electronic states. Shown here isa contour of constant charge density. The golden hexagonal network is associated with the s bands, whereas the six pairs ofgreen lobes above and below the boron plane are associated with the p bands. The p-band charge density extends in boththe parallel and perpendicular directions to form 3D conduction states. (Courtesy of O. Jepsen, adapted from I. I. Mazin etal., ref. 8.) (c) The Fermi surface of MgB2. The vertical sections of cylinders at the corners are associated with the s bands;the more 3D network of tunnels and caves in the center of the zone is associated with the p bands. The letters designate thesymmetry points of the hexagonal Brillouin zone in momentum space. (Adapted from J. Kortus et al., ref. 8.)

Figure 4. Upper critical magnetic field Hc2 for magnesiumdiboride is anisotropic, reflecting the underlying anisotropicelectronic bands. Hc2 is the magnetic field sufficient to de-stroy superconductivity in bulk samples. The data shownhere were inferred from measurements on polycrystalline11

(red) and single crystal12 (black and green) samples. Thelower curves are Hc2

‖c for the magnetic field applied along thec-axis (perpendicular to the basal hexagonal planes in figure3a), and the upper curves are Hc2

♥c for the magnetic field ap-plied within the basal plane. The inset shows the anisotropyratio g [ Hc2

♥c/Hc2‖c from each of these data sets.

Despite being taken from samples ofdiffering form (polycrystalline1,11 andsingle-crystal1,12) and quality (36 K <Tc < 40 K), the Hc2 data show goodagreement. The anisotropy, quantified as the ratio g [Hc2

♥c / Hc2‖c, not only is large, but it has an unusual temper-

ature dependence (see figure 4 inset). At low temperatures,g is about 6, a value close to that expected theoreticallyfrom the geometry of the Fermi surface associated with thes band (figure 3c).1,11 This observation strongly suggeststhat the low-temperature, high-field superconductingstate is dominated by just the s band.

Specific heat measurements of MgB2 below Tc gave thefirst indication that the s and p bands of MgB2 may haveseparate and distinct superconducting gaps.1,13 Figure 5shows the electronic specific heat of MgB2 in zero and highapplied magnetic field. The temperature dependence of theelectronic contribution to the specific heat deviatesmarkedly from that predicted by BCS theory. The most im-portant deviation is the low-temperature shoulder, associ-ated with a second, smaller gap, that is very rapidly sup-pressed by an applied field. The nature and implications ofthese two gaps have been the focus of much of the recentbasic research on MgB2.

Two superconducting gapsThe strong electron–phonon coupling in the 2D s bandsand weak coupling in the 3D p bands lead to a strikingqualitative feature of superconductivity in MgB2: the si-multaneous existence of two energy gaps in the same ma-terial.1,14 The concept of two gaps in a single superconduc-tor has been considered before,15 but MgB2 is the firstexample of a two-gap superconductor in which the effectsare so dramatically expressed.1,10

The two gaps in MgB2 arise naturally from the differ-ent strengths of the electron–phonon coupling in the s andp bands. If the two sets of electrons were independent, thephysics would be straightforward: Two noninteracting su-perconducting condensates share the same crystallineframework but have different transition temperatures anddistinct superconducting properties. The two sets of elec-trons do interact, though, albeit weakly, through scatter-ing from states in one band to states in the other andthrough Coulomb repulsion. This small interaction pro-vides the richness and subtlety that permeates all theproperties of MgB2. For example, a small interactioncauses both bands to become superconducting at the sametemperature; a large interaction, in contrast, would mixthe two bands thoroughly and wash out the distinction intheir energy gaps and dimensionality. In MgB2, the twobands and the two very differently sized superconductinggaps are quite distinct and manifest themselves clearly.

The two gaps can be seen most directly in the super-conducting tunneling behavior. Figure 6a shows the topo-graphic image, taken with a scanning tunneling micro-scope, of a polycrystalline sample of MgB2 with four grainsof different crystallographic orientation. By fixing theSTM above the sample and measuring the differentialconductance as a function of applied voltage, the tunnel-ing spectrum of the sample beneath the STM tip can beobtained. Such spectra were taken on a dense grid of pointsin the indicated box straddling grains 1 and 2. The spec-tra showed a pronounced change exactly at the grainboundary: the spectra from grain 1 show dominant low-voltage conductance peaks, whereas those from grain 2feature dominant high-voltage peaks. In qualitative terms,the positions of the peaks measure the sizes of the super-conducting energy gaps in the MgB2 sample. The remark-able feature of these spectra is their strong sensitivity tothe change in grain orientation relative to the tunnelingdirection. The spectrum in grain 1 is typical of tunnelingalong the c-direction: It probes predominantly the p bandgap, since the s band conducts principally in the basalplane and cannot couple to tunneling currents along the c-direction. The spectrum in grain 2 is typical of tunnelingcurrents in the basal plane, which couple to both the s andp bands. The temperature dependence of the two gaps canbe tracked, as shown in figure 6b, using the directionalsensitivity of the tunneling spectra to identify the gaps.1,16

The tunneling data explain the anomalous specificheat data in figure 5. The behavior near Tc is determinedby the large 2D gap, which produces a step as expected fora conventional one-gap superconductor. The size of thestep is smaller than expected, however, because thesmaller 3D gap of the p bands easily admits thermal ex-citations. At lower temperatures, a large shoulder appearsin the specific heat as the smaller 3D gap cuts off low-energy thermal excitations.1,13

The simultaneous presence of two superconductingcondensates with different gaps and dimensionalities leadsto a host of potentially new phenomena. Each condensatehas its own set of natural characteristic lengths reflectingits own gap size, electron density, and anisotropy. Unrav-eling the physical behavior of the interacting condensatesbecomes a fascinating game of hide-and-seek: Which char-acteristic length controls which property? For example,consider once more the anisotropic Hc2 data shown in fig-ure 4. Near Tc in low magnetic field, both condensates con-tribute to the upper critical field, and defining a single char-

38 March 2003 Physics Today http://www.physicstoday.org

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Figure 5. The electronic contributionto the specific heat Cp presented the

first indication of the presence of twosuperconducting gaps in MgB2. The

data plotted here were taken on a poly-crystalline sample of MgB2 and havebeen adjusted to remove the lattice

contribution.13 The red curve shows theprediction from the Bardeen-Cooper-

Schrieffer theory for a single supercon-ducting gap in zero magnetic field. Theshoulder at low temperatures and fieldsindicates the existence of a second gap.(Adapted from F. Bouquet et al., ref 13.)

acteristic length in terms of a single energy gap is prob-lematic.1,16 At higher field and lower temperature, thesmaller 3D gap is suppressed and the upper critical field isdominated increasingly by the stronger 2D gap. Measure-ments of the anisotropic temperature-dependent uppercritical field reflect this behavior. They show an anomalousupward curvature in the critical field in the basal plane,and a corresponding increase by more than a factor of twoin the anisotropy ratio g as the temperature is lowered fromTc to 5 K (see figure 4 inset).1,11,12

Past, present, and futureIt is ironic that the remarkable superconductivity in MgB2

had to wait until the 21st century to be discovered. All ofthe conditions were ripe more than 40 years ago: Elec-tron–phonon pairing monopolized superconductivity re-search, binary superconductors like Nb3Sn and Nb3Ge werealready well known, and vigorous searches for new inter-metallic superconductors were topical. Magnesium diboridewas not even a new compound in those days; it had beenknown since the early 1950s. Its specific heat was measureddown through 40 K and the rather sparse data were pre-

sented (in tabular form) in 1957.17 Thedetection of the superconducting transi-tion was barely missed. Finally, the the-ory for a superconductor with two dis-tinct gaps was proposed in 1959,15 but layfallow for lack of a concrete example. Onehas to wonder how the world may havebeen different if 40-K superconductivityin MgB2 had been discovered in 1960, be-fore Nb3Sn and Nb–Ti alloys were devel-oped as practical superconductors.Would we now be generating magneticfields, taking magnetic resonance imag-ing scans, measuring tiny magnetic mo-ments, and relaying cell-phone callsusing technology based on MgB2?

As it is, MgB2 has opened our eyesto previously unrealized possibilities forelectron–phonon superconductivity.Higher transition temperatures andother compounds now occupy ourdreams, and novel basic phenomena

such as two-gap superconductivity drive theory and ex-periment in new directions. Unlike the still-controversialcuprates, the physical picture and quantitative theoreticaldescription for MgB2 are now available. We understand theconditions needed for high transition temperatures and forcoexistence of two gaps of very different sizes. Theoristshave begun to propose hypothetical compounds that maysatisfy these conditions, but Nature often frustrates suchdesigns by refusing to let these compounds form. Never-theless, we think we know what we’re looking for. Band-structure and electron–phonon calculations for designercompounds are becoming accessible and may be incisive.

Magnesium diboride opens new avenues for basic andapplied research. On the basic side, can we find other ma-terials with multiple gaps and high transition tempera-tures? The interplay of structure, strongly selective elec-tron–phonon coupling, and weakly interacting bands ofdifferent character may well hold still more subtle secrets.Magnesium diboride itself presents an intellectual chal-lenge: to understand the consequences of two-gap super-conductivity in all its glory. And although we have not dis-cussed the possible applications of MgB2 in this article,MgB2 does appear to be a very promising material. For pure,

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Figure 6. Tunneling experiments clearlyshow the presence of two superconduct-ing gaps in magnesium diboride. (a) Thistopographic image (right) taken by ascanning tunneling microscope shows asection of a polycrystalline sample,150 nm on a side, containing four grains.Tunneling spectra (left) measured with anSTM change dramatically at the bound-ary between grains 1 and 2. The spectraare plotted as the differential conduc-tance dI/dV (where I is the tunneling cur-rent), normalized to the high-voltageconductance. Peaks in the spectra iden-tify the superconducting gaps. (b) Thesensitivity of the spectra to the tunnelingdirection allows the two gaps to be dis-tinguished and followed as a function oftemperature. The red points are the largegap of the two-dimensional s band; theblue are the small gap of the three-dimensional p band. (Adapted from M. Iavarone et al., ref. 16.)

polycrystalline samples, the critical current density—abenchmark of a superconductor’s suitability for many areasof use—approaches 106 A/cm2 at low fields and tempera-tures, and recent work indicates that this value can be in-creased by about an order of magnitude by the judicious ad-dition of impurities.1,4,18 In a similar manner, the uppercritical field has been almost tripled.1,18 The values of thecritical current density and upper critical field start to ex-ceed those found for the industrial standards Nb3Sn andNb–Ti. The quality of MgB2 thin films continues to improve,and there is hope that devices such as superconductingquantum interference devices (SQUIDs) and filters may notbe too difficult to make. And given that the mass density ofMgB2 is low, as is the electrical resistivity of the normalstate, magnets and cables made of MgB2 may be signifi-cantly lighter and cheaper than those of Nb3Sn and Nb–Ti.Such potential looks very promising, especially when com-bined with a readily accessible Tc of about 40 K.

Finally, we note that MgB2 is a poster child for an im-portant observation about condensed matter physics. Su-perconductivity in this simple binary compound lay undis-covered until the new millennium, despite extensivesearches over the past 80 years. Although we now under-stand the basic picture of superconductivity in MgB2, thebehavior was not predicted a priori. The continued exper-imental search for new materials and new behavior in bi-nary, ternary, quaternary, and other compounds is one ofthe most important engines driving progress in condensedmatter physics. To quote Sophocles: “Look and you will findit—what is unsought will go undetected.”

We thank Sergey Bud’ko, Maria Iavarone, and Goran Kara-petrov for providing figures and useful discussions. We bothgratefully acknowledge support from the US Department ofEnergy, Office of Science, Office of Basic Energy Sciences.

References1. A comprehensive review of the first two years’ research on

magnesium diboride can be found in the March 2003 specialissue of Physica C, 385(1–2). That compilation of papers fromnumerous research groups working on MgB2 is a useful re-source for many of the topics discussed in this article.

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40 March 2003 Physics Today