High-temperature superconductivity in iron-based materials€¦ · superconductors. As in the...

REVIEW ARTICLEPUBLISHED ONLINE: 29 AUGUST 2010 | DOI: 10.1038/NPHYS1759

High-temperature superconductivity iniron-based materialsJohnpierre Paglione* and Richard L. Greene

The surprising discovery of superconductivity in layered iron-based materials, with transition temperatures climbing as highas 55K, has led to thousands of publications on this subject over the past two years. Although there is general consensuson the unconventional nature of the Cooper pairing state of these systems, several central questions remain — includingthe role of magnetism, the nature of chemical and structural tuning, and the resultant pairing symmetry — and the searchfor universal properties and principles continues. Here we review the progress of research on iron-based superconductingmaterials, highlighting the main experimental benchmarks that have been reached so far and the important questions thatremain to be conclusively answered.

In February 2008, Hideo Hosono and co-workers reported thediscovery of 26 K superconductivity in fluorine-doped LaFeAsO(ref. 1),marking the beginning ofworldwide efforts to investigate

this new family of superconductors. Although rumours of a 50+ Ksuperconductor swirled around the 2008 APS March meeting inNew Orleans, researchers in Japan and China were busy withexperiments thatwould largely advance this field to its present statusby raising superconducting transition temperature (Tc) values ofLaFeAs(O, F) to 43K by application of pressure2, and then as highas 55K by replacement of La by other rare-earth elements (seeref. 3 for details). Historically, the typically antagonistic relationshipbetween superconductivity and magnetism has led researchersto avoid using magnetic elements — ferromagnetic in particular— as potential building blocks of new superconducting materials.Because elemental iron is strongly magnetic, the discovery of Fe-based superconductors (FeSCs) with high Tc values was completelyunexpected. This has opened a new avenue of research drivenby the fact that our fundamental understanding of the origins ofsuperconductivity needs significant improvement.

This Review Article provides a summary update on some of therecent experimental results and an overview of the status of thefield. Our goal is to highlight important experimental observationsand theoretical perspectives that may lead to a consensus on theunderstanding of superconductivity in the FeSCs. Some resultshave been omitted owing to space and citation limitations, so weencourage the reader to consult more detailed overviews in existingreports3,4. The basic behaviour of several classes of FeSCs is nowknown to be similar, so this Review will cover universal propertiesbut will also focus on the class of intermetallic FeSCs with theThCr2Si2 (122) structure, pointing out any significant differencesfrom the other systems.

Crystal structures and tuning parametersSo far, five different structural classes of FeSCs have beenfound. These structures, shown in Box 1, all share a commonlayered structure based on a planar layer of iron atoms joinedby tetrahedrally coordinated pnictogen (P, As) or chalcogen(S, Se, Te) anions arranged in a stacked sequence separated byalkali, alkaline-earth or rare-earth and oxygen/fluorine ‘blockinglayers’. It is now widely thought that the interaction that leads to

Center for Nanophysics and Advanced Materials, Department of Physics, University of Maryland, College Park, Maryland 20742, USA.*e-mail: [email protected].

the high-Tc superconductivity originates within these commoniron layers, similar in nature to the common copper–oxygenbuilding block found in the copper oxide (cuprate) high-Tcsuperconductors. As in the cuprates, chemical substitution alsoplays a key role in inducing the superconducting phase in ironpnictides. However three key differences are found: (1) in thearrangement of pnictogen/chalcogen anions above and belowthe planar iron layer (see Box 1) as opposed to the planarcopper–oxygen structure of the cuprates; (2) in the ability tosubstitute or dope directly into the active pairing layer; and(3) in the metallic (rather than insulating) multiband natureof the parent compounds. It is these traits, together with thesimilar interplay of magnetism and superconductivity, that markthe iron pnictides and cuprates as distinct, but closely related,superconducting families. The phase diagram of the FeSCs isin fact strikingly similar to those of several other classes ofunconventional superconductors, including the cuprates, organicsand heavy-fermion superconductors, all believed to harbourunconventional (non-phonon-mediated) pairing mechanisms.Although themediator of pairing in these systems remains officiallyunidentified, a large amount of circumstantial evidence pointsto magnetic spin fluctuations: in all cases magnetism must besuppressed, either by pressure or doping, before optimal bulk-phasesuperconductivity appears. Although their more metallic naturemay place them closer to the heavy-fermion systems (metallicmagnetism) than to cuprates (Mott-insulator physics), the strikingresemblance of interpenetrating ground states in these systemsdeserves strong attention in devising a generalized theory ofunconventional superconductivity.

The generic phase diagram of the FeSC systems can be producedby manipulating the chemical or structural properties, using eitherchemical doping/substitution or applied external pressure to drivean antiferromagnetic (AFM), non-superconducting parent com-pound to a superconducting (SC), non-AFM state. A compilationof experimental phase diagrams is presented in Fig. 1 for theBa-based 122 system, so far the most studied of the five familiesand widely thought to capture the main traits of all FeSCs. InBaFe2As2, the systematic substitution of either the alkaline-earth(Ba), transition-metal (Fe) or pnictogen (As) atom with a differentelement almost universally produces the phase diagram presented

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REVIEW ARTICLE NATURE PHYSICS DOI: 10.1038/NPHYS1759

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Figure 1 | Experimental phase diagrams of the BaFe2As2 system.a, Chemical-substitution phase diagram of the BaFe2As2 system, shown forK (ref. 7), Co (ref. 8) and P (ref. 9) substitutions, with the amount ofchemical substitution (x) normalized to overlap the descent of the AFMtransition for simplified comparison of the relative position of the SC phase.The dotted line indicates the structural transition between tetragonal (T)and orthorhombic (O) crystallographic phases observed for Cosubstitution, which is coincident with the paramagnetic (PM) to AFMtransition in the parent compound BaFe2As2 (ref. 8). b, Applied-pressurephase diagram for BaFe2As2 as a function of external pressure appliedunder various levels of hydrostaticity, using diamond anvil cell17,Bridgman18,19 and cubic anvil cell20,21 techniques. Note that the pressureaxis is normalized to overlap the descent of the antiferromagnetictransitions for each experiment for simplified comparison.

in Fig. 1a, composed of coupled AFM and structural transitionsthat are suppressed with substitution and an SC phase that is moreor less centred near the critical concentration where AFM order isdestroyed. This is somewhat different from the known behaviourof fluorine-doped ‘1111’ systems such as LaFeAsO1−xFx (ref. 5),where AFM and SC phases are completely separated as a function ofdoping and do not overlap. However, the coexistence of AFM andSC phases such as reported for SmFeAsO1−xFx (ref. 6) is believedto probably be the more intrinsic property of the generic FeSCphase diagram, motivating efforts to study the 122-type systemsin great detail. The quantitative similarity between phase diagramsproduced by substitutions involving both obvious (that is, K1+ forBa2+; ref. 7) and subtle (that is, Co-3d7 for Fe-3d6; ref. 8) chargedoping, as well as nominally isovalent (P-3p3 for As-4p3; ref. 9)substitutions, is enticing owing to the implied versatility of chemicaltuning parameters available to experimentalists for studying these

systems. Furthermore, it promotes the idea that simple chargedoping is not the sole factor in determining the phase boundaries ofthese systems and that structural tuningmay play a role.

However, subtleties in the electronic structure of thesematerials,as discussed below, make the situation more complex than thatof a simple structural tuning effect. This is highlighted by thesensitivity of the superconducting phase to the particular choiceof ion substituent. For example, superconductivity in the 122-type materials, first shown to occur by Co substitution for Fe inSrFe2As2(ref. 10) and BaFe2As2 (ref. 11), can be stabilized by severaltypes of d-metal substitution. This includes the use of any elementsin the Fe, Co and Ni columns (except, so far, Os; ref. 12), butexcludes Cr (ref. 13), Mn (ref. 14) and Cu (ref. 15), which all actto suppress magnetism without stabilizing a high-Tc SC phase. It isthought that these latter anomalous cases arise for varying reasonsto do with the unfavourable manipulation of Fe bonding andmagnetism, giving clues regarding the correct distinction betweencharge doping and chemical substitution.

Pressure tuning is less well understood. In some cases this pow-erful control parameter is aligned with its chemical-substitutioncounterpart. For instance, in Ba1−xKxFe2As2 a good overlap ex-ists between lattice-parameter variation by applied pressure orK substitution16, enabling conclusions about the roles of latticestructure versus charge doping to be made. In contrast, in pressureexperiments on BaFe2As2, differing experimental conditions im-pose variations from true hydrostatic conditions, making it difficultto generically compare phase diagrams obtained through appliedpressure versus chemical substitution. Figure 1b presents a com-parison of five studies17–21 on our model 122 system using differingtechniques, showing that AFM order is suppressed in a mannersimilar to chemical substitution in all cases shown but with differingrates. Moreover, the pressure range where the superconductingdome is located also varies for each experiment. This is probably dueto the fact that the compressibility of the 122-typematerials is highlyanisotropic, imposing a sensitivity to non-hydrostatic pressureconditions that may alter the evolution of the phase diagram underdiffering experimental conditions. Such a scenario was recentlyshown conclusively in a comparison of pressure experiments usingthe same crystals but different levels of hydrostaticity22. Moreover,a structural phase transition (T0) — from tetragonal at high tem-peratures to orthorhombic at low temperatures — is consistentlyfound to be coupled to the AFM transition at TN , and is eitherpinned directly to TN or is separated in temperature on chemicalsubstitution, as shown by the dashed line in Fig. 1a. Although thisfeature may be a key element in understanding, for instance, thenature of magnetic order as discussed below, it also poses problemsin controlling hydrostaticity in a pressure experiment.

In one extreme case involving pressure-tuning of CaFe2As2, aninstability to another structural phase transition (to the so-calledcollapsed-tetragonal phase) imposes a more severe sensitivity toanisotropic strain conditions, with a pressure-induced SC phaseonly present when non-hydrostatic conditions are imposed23.Although it remains unclear what role structure plays in stabilizingsuperconductivity in CaFe2As2, some theoretical ideas24 suggestinterlayer As–As bonding to be the key ingredient. The sensitivityto hydrostaticity certainly implies that a strain mechanism is atwork, possibly similar to what causes the intermittent appearanceof 20K superconductivity in undoped, unpressurized 122-typeparent compounds25. Indeed, strain effects have been identifiedin studies of twin domain boundaries of BaFe2−xCoxAs2 usingscanning superconducting quantum interference device (SQUID)microscopy, where an enhanced susceptibility at twin boundarieshas been associated with an enhanced superfluid density26. Moregenerally, one of the distinguishing features of the FeSCmaterials isthe fact that the generic phase diagram can be experimentally tunedby any of several different means that allow for a precise control

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NATURE PHYSICS DOI: 10.1038/NPHYS1759 REVIEW ARTICLE

Box 1 |The iron-based superconductor family.

Iron, one of the most common metals on earth, has been knownas a useful element since the aptly named Iron Age. However,it was not until recently that, when combined with elementsfrom the group 15 and 16 columns of the periodic table (named,respectively, the pnictogens, after the Greek verb for choking,and chalcogens, meaning ‘ore formers’), iron-based metals wereshown to readily harbour a new form of high-temperature su-perconductivity. This general family of materials has quicklygrown to be large in size, with well over 50 different compoundsidentified that show a superconducting transition that occursat temperatures approaching 60K, and includes a plethora ofdifferent variations of iron- and nickel-based systems. So far, fiveunique crystallographic structures have been shown to supportsuperconductivity. As shown in Fig. B1a, these structures allpossess tetragonal symmetry at room temperature and rangefrom the simplest α-PbO-type binary element structure to morecomplicated quinternary structures composed of elements thatspan the entire periodic table.

The key ingredient is a quasi-two-dimensional layer consistingof a square lattice of iron atoms with tetrahedrally coordinatedbonds to either phosphorus, arsenic, selenium or tellurium anionsthat are staggered above and below the iron lattice to form achequerboard pattern that doubles the unit-cell size, as shownin Fig. B1b. These slabs are either simply stacked together, as inFeSe, or are separated by spacer layers using alkali (for example,Li), alkaline-earth (for example, Ba), rare-earth oxide/fluoride(for example, LaO or SrF) or more complicated perovskite-typecombinations (for example, Sr3Sc2O5). These so-called blockinglayers provide a quasi-two-dimensional character to the crystal

because they form atomic bonds of more ionic character with theFeAs layer, whereas the FeAs-type layer itself is held together bya combination of covalent (that is, Fe–As) and metallic (that is,Fe–Fe) bonding.

In the iron-basedmaterials, the commonFeAs building block isconsidered a critical component to stabilizing superconductivity.Because of the combination of strong bonding between Fe–Feand Fe–As sites (and even interlayer As–As in the 122-typesystems), the geometry of the FeAs4 tetrahedra plays a crucial rolein determining the electronic and magnetic properties of thesesystems. For instance, the two As–Fe–As tetrahedral bond anglesseem to play a crucial role in optimizing the superconductingtransition temperature (see the main text), with the highest Tcvalues found only when this geometry is closest to the ideal valueof∼109.47◦.

Long-range magnetic order also shares a similar patternin all of the FeAs-based superconducting systems. As shownin the projection of the square lattice in Fig. B1b, the ironsublattice undergoes magnetic ordering with an arrangementconsisting of spins ferromagnetically arranged along onechain of nearest neighbours within the iron lattice plane,and antiferromagnetically arranged along the other direc-tion. This is shown on a tetragonal lattice in the figure,but actually only occurs after these systems undergo anorthorhombic distortion as explained in the main text. Inthe orthorhombic state, the distance between iron atoms withferromagnetically aligned nearest-neighbour spins (highlightedin Fig. B1b) shortens by approximately 1% as compared with theperpendicular direction.

FeSe

LiFeAsSrFe2As2

Sr3Sc2O5Fe2As2

LaFeAsO/SrFeAsF

a b

Figure B1 | Crystallographic and magnetic structures of the iron-based superconductors. a, The five tetragonal structures known to supportsuperconductivity. b, The active planar iron layer common to all superconducting compounds, with iron ions shown in red and pnictogen/chalcogenanions shown in gold. The dashed line indicates the size of the unit cell of the FeAs-type slab, which includes two iron atoms owing to the staggeredanion positions, and the ordered spin arrangement for FeAs-based materials is indicated by arrows (that is, not shown for FeTe).

of structural parameters, disorder location, chemical bonding anddensity. This is one of the key properties that has led to arapid but in-depth understanding of these materials. In due time,controlled experimental comparisons — for instance of Hall effect

(carrier density) under pressure versus doping, of different chemicalsubstitution series and further understanding of the local nature ofchemical substitution — will help pinpoint the important tuningparameters for these systems.





Electronic structureWith an interplay of magnetic and electronic interactions probablyplaying an integral role in determining the shape of the phasediagram of all FeSC systems, much work has gone into determiningthemagnetic and electronic structures of thesematerials. In general,these materials are well described as consisting of two-dimensional(2D) metallic sheets derived from Fe d states hybridized withAs p-orbital-derived bands, sitting in a quasi-ionic frameworkcomposed of rare-earth, oxygen, alkali or alkaline-earth blockinglayers (see Box 1). This arrangement unites to produce a metallicmaterial with nominal Fe valence of 2+, low carrier concentrationand high electronic density of states dominated by Fe d states27.On the basis of this FeAs-layered framework, the electronic bandstructure has been calculated using the local density approximation(see ref. 27 for an overview), showing that the electronic propertiesare dominated by five Fe d states at the Fermi energy, with a Fermisurface (FS) consisting of at least four quasi-2D electron and holecylinders (see Box 2). These consist of two hole pockets centred atthe Brillouin zone (BZ) centre and two electron pockets centred at(0,±π) and (±π,0) in the tetragonal unit cell. Two non-equivalentAs positions (staggered above and below the Fe lattice) result in thefolding of the BZ to include two Fe atoms per unit cell and to putthe electron pockets at (±π,±π) as shown in Fig. B2b, the samedirection of AFM ordering vector as discussed below. A fifth holeband is also proposed to sit at (0,±π) in the folded BZ, and itspresencemay be very sensitive to structural details28.

The qualitative agreement with experiment is remarkablygood, as shown by several angle-resolved photoemission spec-troscopy (ARPES) and quantum oscillation measurements. InitialARPES studies on LaFePO (ref. 29), NdFeAsO0.9F0.1(ref. 30) andBa0.6K0.4Fe2As2 (ref. 31) all confirmed the predicted band struc-ture consisting of hole pockets at the BZ centre and electronpockets at the BZ corners. Quantum oscillation experiments car-ried out on paramagnetic P-doped BaFe2As2 (ref. 32) also revealan unreconstructed FS consistent with this basic structure, andmeasurements on the BaFe2As2, SrFe2As2 and CaFe2As2 parentcompounds are also consistent if we take into account the BZreconstruction due to AFM ordering33. As is usual, the details revealmore: simple 2D models may not capture subtle but importantdetails of the true band structure, and three-dimensional (3D)aspects may have important implications for magnetism and su-perconductivity. Although ARPES is a surface probe, it is capableof probing kz dispersion to a limited extent, and several studies4have reported strong modulation along the kz direction at theBZ centre in agreement with theory34. Also, Compton scatteringmeasurements, which are a bulk probe of the occupied states, areconsistent with strong three-dimensionality in optimally dopedBaFe2−xCoxAs2 (ref. 35).

Despite being another area of active debate, the effect ofhole/electron doping on the electronic structure is fairly wellcaptured by a rigid-band picture: the basic FS topology iskept with both electron (that is, in BaFe2−xCoxAs2(ref. 36))and hole (that is, in Ba1−xKxFe2As2 (ref. 37)) doping, with thesize of FS pockets changing accordingly and with reasonablecontinuity observedwhen crossing between each case38. Once again,however, it seems that charge doping is not the only mechanismby which this tuning can be achieved. For instance, isovalentsubstitutions would not be expected to mimic charge-dopingeffects; however, the nominally isovalent substitutions of P forAs (ref. 39) and Ru for Fe (ref. 40) in BaFe2As2 indeed causesubstantial changes to the Hall coefficient, even changing signin the latter case. Moreover, a comparable scaling of FS pocketsize has been shown to occur as a function of isovalent As/Psubstitution32, and density functional theory (DFT) calculationssuggest that the main effect of charge doping is not on thedensity of states, but rather on the disruption of nesting and

the relative size of electron and hole pockets34. Beyond isovalentsubstitution, a recent DFT study of the local nature of d-electron‘dopant’ ions (including the likes of Co and Ni) concludedthat the extra electrons actually remain predominantly localizedat the substituent site, and may act mainly to disrupt nestingproperties rather than changing charge density41. This remains tobe verified experimentally.

More profound changes in band structure may also be atplay. ARPES studies of BaFe2−xCoxAs2 provide indications of apossible Lifshitz transition where hole pockets disappear, enablingsuperconductivity to thrive42. A change in effective dimensionalityacross theAFM transition— with the development of a 3D ellipsoidin CaFe2As2 below T0 — has been suggested to be importantfor superconductivity43, but is in conflict with the observationof significant 3D structure in BaFe2−xCoxAs2 outside the AFMphase44. Furthermore, a qualitative change in band structure seemsto occur as a function of Co doping at the onset of the SCphase, as observed in ARPES (ref. 42) and Hall data45, and is alsosupported by transport data46.

The connection between structural details of FeSC materialsand their seemingly sensitive electronics is an important aspect ofsuperconductivity in the FeSCs. An empirical relationship betweenthe tetrahedral bond angle of the As–Fe–As layer and Tc values fordifferent FeSCs was recognized early on, with optimal Tc valuessuggested to be promoted by ideal tetrahedral geometry47. This hasimportant implications, both theoretically and in practical terms: aclose relationship between structure and superconductivity, director indirect, places constraints on both the theoretical understandingof the pairing interaction and the promise of superconductors withhigher Tc values. Although it seems that this relationship is notuniversal (a notable exception includes CsFe2As2, with Tc = 2.6Kand As–Fe–As bond angle very close to the ideal value of 109.47◦;ref. 48), it remains true that the highest-Tc FeSCs are still clusteredclose to the ideal tetrahedron geometry. A proposed sensitivityof electronic structure and/or magnetic interactions to details ofthe internal structure of the Fe–As layers is probably relevant tounravelling this puzzle. For example, calculations of the dependenceof nesting in the band structure, and consequently pairing in aspin-fluctuation-mediated scenario, show a sensitivity of an extra(third) hole pocket to pnictogen height above the Fe plane withconsequences for pairing symmetry28.

MagnetismThe nature of magnetism in the FeSC parent compounds is ahotly debated topic, largely owing to its implications for thepairing mechanism: the electronic structure suggests that the samemagnetic interactions that drive the AFM ordering also producethe pairing interaction for superconductivity49. As predicted beforeexperiments50, AFM order in all FeAs-based superconductingsystems is found to have a wave vector directed along (π,π)in the tetragonal unit cell with a real-space spin arrangementconsisting of AFM stripes along one direction of the Fe sublatticeand ferromagnetic stripes along the other (see Box 1), with anordered moment typically smaller than one Bohr magneton51,52.This is much smaller than that of metallic Fe, presenting achallenge for first-principles calculations, which predict a muchlarger moment when using the real unit-cell parameters27. Earlyon, theoretical calculations found these materials to lie neara Stoner instability, suggesting inherent itinerant magnetism27,which could potentially explain the consistent overestimates of theordered moment size. However, this ordering arrangement alsofalls naturally out of a local-moment ‘J1–J2’ model with nearest-(J1)and next-nearest-(J2) neighbour exchange interactions such thatJ1<2J2 (ref. 53), and hence a lot of effort has gone into determiningwhether such a localized model holds any validity for a systemthat is clearly metallic.





NATURE PHYSICS DOI: 10.1038/NPHYS1759 REVIEW ARTICLE

Box 2 | Electronic band structure and pairing symmetry.

Themanner inwhich electrons in a solid behave, in the presence ofone another and the surrounding ionic lattice, is well captured byone of the staples of condensed-matter physics known as band the-ory. A metal’s band structure can convey a simple yet quantitativedescription of its electronic, optical and structural properties, andis the basis for understanding many exotic phenomena. In metals,the energy states that participate in determining most propertiesof a material lie in close proximity to the Fermi energy, EF, thelevel below which available energy states are filled (and thereforeunavailable) owing to Pauli exclusion.

The band structures of the iron-based superconducting ma-terials have been calculated using first-principles DFT, findinggood general agreement with experimental measurements (seemain text). The dominant contribution to the electronic density ofstates at EF derives from metallic bonding of the iron d-electronorbitals in the iron–pnictogen (or chalcogen) layer. These formseveral bands that cross EF, both electron- and hole-like, resultingin a multiband system dominated by iron d character. As shownin Fig. B2a for the case of Co-doped BaFe2As2, the electronicstructure is visualized as several distinct sheets of FSs within theBZ, each corresponding to a different band that crosses EF.

Instabilities of this electronic structure to bothmagnetic order-ing and superconducting pairing are widely believed to be at theheart of the exotic properties of the iron-based superconductingmaterials. For instance, in Fig. B2a we can see that a magneticordering vector that spans from the centre of the BZ at k= (0,0)(0 point) to the corner at k= (π,π) (M point) will easily nest acircle of points on each of two different FS sheets (for example,purple and red sheets), resulting in a spin-density wave order thatis driven by properties of the band structure.

Superconductivity is another very well known phenomenonthat also results in an ‘ordered’ state that has a strong tie to theband structure. The superconducting order parameter (OP) 1,or ‘gap function’, is a complex function with both amplitude andphase that describes the macroscopic quantum state of Cooperpairs. Its amplitude can in general depend on momentum direc-tion and can change sign through its phase component, but in thesimplest case is isotropic (s-wave symmetry) and therefore has aconstant value for all momenta. Details of the pairing potentialcan instil a less simple case that involves a variation of amplitudeas a function of k, or even a variation in phase that results in achange in the sign of 1 that necessitates the presence of zeroesor ‘nodes’ that can take on lower symmetries (d wave, f wave,and so on).

Figure B2b presents three possible scenarios for the super-conducting OP symmetry in the iron-based superconductors.With the simplest s-wave gap symmetry (that is, with constantphase), widely ruled out by experimental evidence (see maintext), more complicated scenarios are required to explain allobserved properties. In particular, circumstantial evidence sup-ports a picture where a change in the sign of 1 must occursomewhere in the BZ. With multiple FSs, which is the casefor FeAs-based materials, this can be realized by positioninga node either away from the Fermi energy (so-called s±) ordirectly at the Fermi energy (d wave or lower symmetry).Moreover, a modulation of the gap amplitude can occur suchthat, even in the s-wave case, so-called accidental nodes arepresent on at least some FSs, enabling low-energy excitationsto flourish even at temperatures much below the energy ofthe gap.

s wave

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Figure B2 | Fermiology and superconducting OP symmetry of 122-type iron-based superconductors. a, FSs of BaFe2As2 with 10% substitution ofCo, calculated using DFT using experimental atomic positions and drawn using the folded BZ representation with two Fe per unit cell (from ref. 49).The hole-like FS pockets (purple and blue) are centred on the 0 point [k= (0,0)] and the electron-like surfaces are at the M point ([k= (π,π)).b, Schematic of the two-dimensional (kx–ky) projection of the BZ of superconducting FeAs-based materials, with multiple bands reduced to singlehole (h) and electron (e) pockets. The proposed multiband pairing gap symmetries, drawn as shaded regions on hole (red) and electron (blue)pockets, are shown for an s± structure with isotropic gaps (left) and anisotropic gaps with accidental nodes on the electron pocket (middle), and fora d-wave symmetry (right).

From the itinerant side, most models focus on a spin-densitywave (SDW) instability of the FS. Although there are not manydirect observations of an SDW energy gap, optical studies ofBaFe2As2 and SrFe2As2 have indeed shown evidence for gappingof the FS below TN (ref. 54). It is widely thought that the SDWinstability arises from the nesting of two FS pockets by a largeQ = (π,π) vector that is commensurate with the structure. Thisvector corresponds to the magnetic ordering vector measuredthroughout the FeAs-based parent compounds as well as thatfor magnetic fluctuations in the superconducting compounds51,52.

There is varied, but good, evidence for (π,π) FS nesting acrossthe entire FeSC family, as indicated by ARPES measurementsof BaFe2−xCoxAs2 (refs 38,55) and Ba1−xKxFe2As2 (refs 31,37)and quantum oscillation measurements in LaFePO (ref. 56)and overdoped BaFe2As2−xPx (ref. 57). In addition, the closelyrelated material FeTe also exhibits nesting in the same (π,π)direction, even though its magnetic ordering vector is shifted by45◦ at (π,0) (ref. 58).

In the parent compounds, there are differing results regardingthe change in band structure through the magnetic transition as





interpreted using ARPES data, but bulkmeasurements of electronicstructure are more consistent. All studies33 observe small FSpockets consistent with band-structure calculations that considera conventional band-folding picture of the AFM ground stateinvolving quasiparticles in a conventional SDW model. Althoughthe general picture is well fitted with an SDW model, there areproblemswithmatching to a purely itinerant scenario. In particular,there is significant, non-trivial reconstruction of the FS below TNthat goes beyond simple band-folding (for example, see ARPES dataon SrFe2As2 and BaFe2As2 (ref. 59). Theoretically, these concernscan be taken into account in an itinerant scenario by consideringdetails of the multiband structure60,61, with the non-trivial bandfolding and metallic nature of the FeSCs probably a result ofpartial gapping of the FS.

From the local side, magnetic frustration is another wayto explain the anomalously low moment size. Although thesematerials are indeed metals, local-moment models at the veryleast find use in describing experimental results. Neutron-scatteringmeasurements of CaFe2As2 have revealed magnetic spin-waveexcitations to live up to ∼200meV, with low-energy modes thatcan be phenomenologically fitted to a local-moment 3DHeisenbergmodel62,63. One study62 observes strong damping at high energiesconsistent with the presence of particle–hole excitations, whereasanother63 does not observe this damping but argues that a largein-plane anisotropy of local-moment interactions, together with theincompatibility of a spin-1/2model with even-numbered electronsin Fe-3d6, necessitates the presence of an itinerant component.Above all, it is safe to say that these materials are ‘itinerant bydefinition’51, because calculations suggest that all Fe-based bandscross the Fermi energy and thus intimately involve conductionelectrons in forming the magnetic state. However, we shouldnot exclude the applicability of other alternative scenarios (seeref. 52 for details), including orbital order64, coexistent65 itinerantelectrons and local moments, or an admixture of both localcoupling and itinerant one-electron interactions66. In the lattercase, the possibility that a nesting feature merely directs theordering wave vector of local moments formed independent ofthe FS morphology is a tantalizing prospect that explains many ofthe observed properties.

Regardless of the exact nature of magnetic order, it is clearthat magnetostructural coupling is prevalent throughout the FeSCfamily in the form of coupled magnetic and structural transi-tions. This is generally understood to be driven by magneticinteractions27,53. However, a peculiarity of the coupled transi-tions is that, aside from the case of the 122-type parent com-pounds where TN and T0 coincide exactly, the structural andmagnetic phase transitions are positioned at different temper-atures in 1111-type compounds, with the structural transitionactually preceding the magnetic transition67. A comparison ofthis phenomenon in samples of CeFeAsO with differing lev-els of disorder (polycrystal, cluster, single crystal) has shownthe splitting to decrease (from 18 to 6K) with improved sam-ple quality68. Considering that the splitting between TN andT0 is established in 122-type compounds only after chemicalsubstitution8,69, it is tempting to conclude that disorder is thecause of the splitting. However, an intrinsic mechanism for thissplitting cannot be ruled out, especially considering the earlyprediction of an Ising phase transition that should precede TN(ref. 70). Furthermore, an investigation of Ba0.84K0.16Fe2As2 sam-ples with both magnetic/structural and superconducting tran-sitions has shown that the magnetic and structural transitionsare indeed separated in crystals with excellent homogeneity71,as opposed to previous reports. It will thus be interestingto see whether experiments that tune effective dimensionalityand/or magnetic coupling will reveal further insight into the na-ture of this splitting.

Finally, a direct coupling between structural distortion andmagnetism has also been shown in P-doped CeFeAsO, whereneutron scattering measurements reveal an ordered AFM momentof Fe to be linearly proportional to orthorhombicity (that is,lattice-constant ratio a/b) as a function of P concentration72.Although seemingly in line with the strong magnetostructuralcoupling discussed above, this result remains highly enigmaticowing to the apparent contradictionwith first-order Landau theory,which forbids a linear relationship between these vector and scalarOPs. This strange but apparently universal coupling remains as animportant topic in our understanding of the relationship betweenmagnetism and structure in the FeAs-basedmaterials.

Superconducting state— pairing symmetryAs for the high-Tc cuprates, the fundamentalmechanism that causesthe high-temperature superconductivity in the FeSCs is a questionof primary importance. In both cases the experimental evidence sofar favours an unconventional pairing mechanism closely tied tomagnetism. Although the exact nature of the pairing is not knownin either system at present, many experiments aimed to determinethe pairing symmetry have been carried out. For the cuprates,the experimental evidence favours a singlet d-wave symmetry thatinvolves a change in sign of the superconducting OP phase atnodal points situated at the Fermi energy (EF) and directed along(π,π) in the simple 2D cuprate band structure. For the FeSCs,the initial measurements31,73 probing the OP symmetry pointedto a fully gapped OP consistent with a fully symmetric s-wavesymmetry. In comparison to cuprates and other magneticallymediated superconductors, this came as a surprise. However, theOP symmetry of FeSCs was in fact predicted theoretically to haves-wave symmetry, but with a sign change that occurs betweendifferent bands in the complex multiband electronic structure. Thisis the so-called s± state, calculated before experiments50 (see ref. 49and Box 2 for more details), which will be predominantly discussedbelow in the context of experimental work.

Experiments that probe the symmetry of the SC phaseprovide important information about the energy and momentumdependence of Cooper pairing, and are therefore pivotal to helpingelucidate the pairing mechanism in this new class of high-Tcsuperconductors. Owing to the vastness of the iron pnictide familyand the nature of chemical substitution, one limitation so far isthat many experiments have been carried out on different systemsor different chemical compositions of the same crystalline system,and thus make comparisons difficult. However there is surprisinglygood consistency, enabling general conclusions to be drawn fromseveral experiments. For instance, NMR experiments were quick todetermine from Knight shift measurements that the SC state spinsymmetry is probably singlet74–76, implying an even OP symmetry(that is, s wave, d wave and so on). So far, this experiment hasbeen done on the main members of the FeSC family, includingsamples of the 1111- (refs 74,75), 122- (ref. 76) and 11-type (ref. 77)systems, so it is reasonable to assume that SC in the iron pnictidesis universally spin singlet.

Determining the nature of the orbital OP symmetry, however,is much more complex and is at present the focus of most research.First, themuch-discussed s± state shares the same symmetry class asthe simple s-wave case, reducing the number of available probes ableto distinguish the two. Moreover, owing to the multi-orbital natureof the FeSCs and their nesting properties, anisotropic (extended)s- and d-wave states are nearly degenerate78, making it difficult toidentify the underlying symmetry even if experiments determinethe presence of nodes in the gap function. Experiments to probethe orbital symmetry usually probe either the amplitude or thephase of the OP. For the cuprates, the phase experiments gavethe most convincing evidence for a sign-changing d-wave (dx2−y2)symmetry: corner junction tunnelling and SQUID experiments,





NATURE PHYSICS DOI: 10.1038/NPHYS1759 REVIEW ARTICLEobservation of half-integer flux quantum from polycrystallinematerials or bicrystal ab-plane oriented films and absence of c-axisJosephson effect with an s-wave SC were all taken as evidencefor d-wave symmetry.

For the FeSCs, only a few phase experiments have been doneso far. In polycrystalline 1111 no half-integer flux was found bya scanning SQUID experiment79, and a robust c-axis Josephsoneffect was found between Pb and K-doped BaFe2As2 (ref. 80),which rules out a predominant d-wave symmetry in these materialsat the measured K concentrations. However, to distinguish aconventional s-wave state from s± is not as straightforward as for ad-wave state. Several proposals for tunnelling/SQUID experimentshave been made81–83, but all require junction geometries moredifficult to prepare than a simpler corner junction, and noexperimental results have so far been reported. One new typeof phase experiment has been reported84, where half-integer fluxquantum jumps were observed in a loop formed by Nb andpolycrystalline NdFeAsO0.88F0.12. These jumps were interpreted asarising from π phase shifts at a few polycrystal boundaries ascurrent is passed through the sample, which could only occur if thesymmetry involves a sign-changing s± state. A d-wave symmetrywas ruled out because many more jumps would be expected inthis case, and these were not observed by the scanning SQUIDexperiment79. Another phase-sensitive experiment, just reported85on a single crystal of Fe(Se, Te), uses spectroscopic-imagingscanning tunnelling microscopy to determine the sign of the OPgap by themagnetic-field dependence of the quasiparticle scatteringstrength. Because of the coherence factors, the scattering amplitudesare different for sign-changing and sign-constant symmetries. InFe(Se, Te), it was found that the sign of the gap is reversed betweenthe electron and hole pockets85. This, along with an absence oflow-energy quasiparticle excitations in the tunnelling gap (as wouldbe seen from the nodes in a d-wave SC), strongly suggests an s±state. Together, all of these results favour the s± state in the FeSCs,but definitive phase experiments on more materials are needed toconclusively settle the case.

Neutron scattering has been instrumental in helping clarifynot only the magnetic properties51, but also the interplay ofmagnetism and superconductivity in the FeSCs. For instance,strong evidence now exists for the competitive nature of AFMand SC coexistent phases in BaFe2−xCoxAs2, as determined by theobservation of a reduction of the static Fe moment on enteringthe SC state52. A systematic study of the same nature86, comparingexperimental results to a mean-field Ginsburg–Landau model,found this behaviour to be inconsistent with a non-sign-changing s-wave symmetry, providing further support for the s± gap structure.

The observation of a collective magnetic-resonance modethat appears below the SC transition temperature is a well-known feature found by inelastic neutron-scattering experimentsin cuprate, heavy-fermion and, most recently, FeSC compounds.This feature, which seems to universally relate the energy of theresonance mode to the SC energy gap87, has now been clearlyobserved in superconducting 1111- (ref. 88), 122- (refs 89–92) and11-type (refs 93,94) compounds, providing important implicationsfor the symmetry of the OP (ref. 95). As shown in Fig. 2,the resonance observed in several experiments follows a verystrong correlation with the SC state, as indicated by a scaling ofthe resonance energy with Tc. Because this relationship appearsexclusively in nearly magnetic unconventional superconductors87,it is considered either (optimistically) a strong signature ofmagnetically mediated pairing, or (pessimistically) an independentremnant of nearby magnetic order. In the first case, it is infact possible to extract gap symmetry and phase informationfrom the momentum dependence of the resonance by comparingwith predictions for several differing gap symmetries96. In thesecond case, the resonance appears as a consequence of the

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Figure 2 |Universal experimentally scalable quantities of FeAs-basedsuperconducting materials. a, Absolute size of the measured jump inelectronic specific heat at the superconducting transition in severalmembers of 11-, 122- and 1111-type FeSC compounds plotted as a functionof Tc. Originally identified in Co- and Ni-doped BaFe2As2 (ref. 122) andsubsequently verified in K- (ref. 123), Co- (refs 115,124), Rh-, Pd- (ref. 125)and Pt-doped12 BaFe2As2 systems, as well as FeTe0.85S0.15 (ref. 126),RFePO (refs 127,128), FeSe0.5Te0.5 (ref. 129) and LaFeAsO0.89F0.11

(ref. 130) superconductors, this thermodynamic quantity seems to scalequadratically with Tc in all cases, as demonstrated by the solid line fitted toa quadratic power law. b, Energy of magnetic neutron resonance measuredat a commensurate (π,π) wave vector in several FeSC systems including1111- (ref. 88), 122- (refs 89–92) and 11-type (refs 93,94) compounds,plotted as a function of Tc. The solid line is a linear fit to all data, indicatingthat the resonance energy scales linearly with Tc.

reduction of the rate of magnon decay through conductionelectrons owing to the opening of the SC gap at Tc. Althoughthe true relationship between the resonance and superconductivityremains unclear, these opposing scenarios can be delineated byexperimental determination of any fine structure of the resonancemode. So far, neutron experiments carried out in high magneticfields do not yet reveal any splitting97. Nonetheless, the strikingobservation of a resonance at the (π,π) nesting vector in FeSe0.4Te0.6





(ref. 93), despite the nearby magnetic order of FeTe that livesat a different ordering vector (π,0), provokes an interpretationthat involves spin fluctuations at least circumstantially tiedto superconductivity.

For amplitude-sensitive experiments, NMR experiments werethe first to probe the OP symmetry by considering the temperaturedependence of the nuclear relaxation rate 1/T1 below Tc, with avariety of results dominated by ∼T 3 behaviour (see refs 3,4), butwith exceptions including much lower (∼T ) power laws consistentwith a nodal OP structure in BaFe2As2−xPx and higher (∼T 5) powerlaws more consistent with activated behaviour in Ba1−xKxFe2As2(ref. 98). The intermediate (∼T 3) power laws, although consistentwith a 2D line-node model, could also be mimicking a crossoverbehaviour expected in a s± gap model that accounts for disorderscattering, with exponential behaviour in 1/T1 expected only atlow temperatures95,99.

Measurements of thermal conductivity at temperatures ap-proaching absolute zero are one of the best bulk-probe techniquesfor studying low-lying quasiparticle excitations in a superconduc-tor, with the ability to provide strong constraints on the pairingsymmetry. For a fully gapped single-band s-wave superconductor,the electronic thermal conductivity follows an activated behaviourin both temperature and field (H ) dependence owing to the fullgapping of the FS, going exponentially to zero with T and H forT � Tc and H �Hc2 (with Hc2 being the upper critical field). Fora superconductor with nodes (see Box 2), a T -linear electroniccomponent arises owing to residual nodal quasiparticle excitationsinduced by impurity scattering. Also, magnetic field is much moreeffective in activating thermal carriers, with the Volovik effectimposing a strong enhancement in nodal excitations that increasesas H 1/2. In a multiband superconductor, particularly with the s±structure, the exact expectation for thermal quantities is difficult todetermine owing to the complex interplay of impurity, inter- andintra-band scattering, but has been addressed100.

Several low-temperature thermal-conductivity measurementshave now been reported for the FeSCs, with a variety of behavioursobserved. Figure 3 presents a summary of the magnetic-fielddependence of thermal conductivity measured in several Ba-based122 compounds in the low-temperature (T = 0) limit, plotted asa function of reduced field to show both the T -linear component(H = 0 intercept) and the field dependence in the T = 0 limit101–106.As shown, even in this constrained set of compounds there is awidely varying set of behaviours, spanning the range between thestandard fully gapped and nodal OP expectations described above.So far, this is one of the most puzzling results from OP symmetry-sensitive experiments: even within a controlled substitution series,such as in BaFe2−xCoxAs2, there is a strong evolution of the fieldenhancement of thermal carriers with doping, suggestive of anevolution of the gap structure102. Even more perplexing is thefact that, in contrast to Co- and Ni-doped BaFe2As2, a T -linearterm is observable in BaFe2(As0.67P0.32)2 (ref. 106), signifying thatthe development of nodes in the gap structure is sensitive tothe type of chemical substitution. Furthermore, the ‘extremelyoverdoped’ stoichiometric compound KFe2As2 also seems to showlow-energy excitations consistent with line nodes105, as opposed toBa1−xKxFe2As2 near optimal K concentration101.

However, this apparently confusing situation may be consistentwith the proposed s± gap structure due to the developmentof accidental nodes (or at least deep minima) in the OPunder certain conditions.

For instance, it has been shown theoretically that disordercan ‘lift’ existing nodes in an s± OP owing to the averaging ofanisotropy by intraband scattering107. It was also suggested thatnodes can appear when a third hole pocket at (π,π) is absent,or more generally when variations in the electronic structure areimposed by its sensitivity to the Fe–As tetrahedral bond geometry.

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Figure 3 | Electronic thermal conductivity of FeAs-based systems in thesuperconducting state. a,b, Thermal-conductivity data in the T=0 limit ofseveral members of the chemically substituted BaFe2As2 family are plottednormalized to normal-state values (that is, at Hc2) as a function of appliedfield normalized to upper-critical-field values. Experimental data setsinclude Ba1−xKxFe2As2 (ref. 101), KFe2As2 (ref. 105), BaFe2−xCoxAs2 forbasal plane102 and c-axis current orientations108, BaFe2−xNixAs2 (ref. 104)and BaFe2As2−xPx (ref. 106). These are separated for clarity purposes intodata sets that do not exhibit a residual (that is, y-intercept) contributionattributable to low-energy quasiparticle excitations at zero field (a) anddata sets that do show a clear residual contribution at zero field (b). Notethat all systems that exhibit a residual contribution (right) also showexceptionally similar field dependence, closely following the expectation foran unconventional superconductor with line nodes in its gap symmetry(dotted lines).

For instance, it is claimed that the tendency towards magnetismbecomes stronger with increasing pnictogen height above the Feplane, causingmultiple spin-fluctuationmodes to conspire to resultin either a fully gapped OP or one with nodes28.

Both the temperature and field dependencies of thermalconductivity have been calculated for several combinations oftwo-band s-wave symmetries, including non-sign-changing andsign-changing cases with anisotropies and varying rates of disorderscattering imposed100. A plethora of expectations are found, fromfully activated behaviour in an isotropic two-gap (s++ or s±)state with no disorder to a finite non-universal residual electronicterm in an anisotropic two-gap (s±) state that depends non-monotonically on disorder. A strong field dependence at small Hrules out a clean s± state for 122-type materials but is consistentwith pair-breaking scattering. However, the pair-breaking wouldhave to be unphysically strong (note that Ba1−xKxFe2As2 andBaFe2−xCoxAs2 probably have very different levels of disorderowing to ion-replacement location). Therefore, the conclusionis that the 122-type materials probably have a multiband A1g(s-wave) symmetry state with a highly anisotropic gap on one FS(ref. 100). Although this seems to be inconsistent with ARPESexperiments, which so far show only isotropic gap structures30,31,55,the situation may be reconciled in a scenario where the SCOP has a strong 3D momentum dependence. In particular, veryrecent thermal conductivity experiments on BaFe2−xCoxAs2 inthe zero-temperature limit have uncovered a finite residual T -linear component when thermal currents are directed along thecrystallographic c axis108, which is consistent with the presenceof nodes on part of the FS. Because the normalized (relativeto the normal state) residual conductivity quickly rises for bothcurrent directions with field and even becomes isotropic at ∼25%of Hc2, a scenario where an effectively 2D FS harbours a gap





NATURE PHYSICS DOI: 10.1038/NPHYS1759 REVIEW ARTICLEwith non-zero minima and a more 3D surface (that is warpedenough to contribute to c-axis transport) harbours a gap withnodes is suggested108. Although the experiment cannot distinguishbetween a structure with nodes positioned at zero- or finite-valuedkz, theoretical predictions for a proximity-induced gap would beconsistent with c-axis nodes109. What is most striking, however,is that the residual conductivity is most pronounced away fromoptimal doping, which is either an extrinsic effect due to animpurity- or disorder-induced normal-state contribution (possiblyrelated to the residual heat capacity discussed below), or anintrinsic signature of the nature of the SC gap. As pointed outin ref. 108, ‘modulation is a sign of weakness’, which translatesto the provocative idea that deviations from two-dimensionalitymay weaken the SC state in the iron pnictides. Nevertheless,future experiments should help settle these issues. Specifically,magnetic-field angle-resolved thermal-conductivity and specific-heat studies should delineate the position(s) of nodes and theOP symmetry. Recent specific-heat measurements on the relatedmaterial Fe1+xSe0.4Te0.6 have indeed revealed a four-fold oscillationin the basal plane consistent with either nodes or deep minimain the gap structure110.

Temperature-dependent penetration-depth experiments havealso given a wide disparity of results, including activated (exponen-tial) behaviour in PrFeAsO1−y and SmFeAsO1−xFy, and power-lawbehaviour in 1111- and 122-type FeSCs and in chalcogenide- andphosphide-based systems (see ref. 4 for detailed references). Thesevariations can possibly be explained as due to impurities or otherdisorder, because the T dependence of the penetration depth isvery sensitive to disorder and paramagnetic contributions. Thiswas shown systematically in the 122 system, where the exact tem-perature dependence was shown to vary as a function of intrinsicdisorder in the case of Ba1−xKxFe2As2 (ref. 111) and as a function ofdisorder imposed by irradiation in the case of Co- and Ni-dopedBaFe2As2 (ref. 112). Also, the activated behaviour in Pr- andSm-based 1111-type materials is put into question in a study onLa- and Nd-based 1111-type crystals113, where the subtraction of aparamagnetic contribution reveals a quadratic temperature depen-dence of the London penetration depth. These corrected data canbe fitted with a two-gap s-wave model, but issues with the extracted1/kBTc ratios being smaller than the Bardeen–Cooper–Schrieffer(BCS) expectations and deviations of the fits near Tc call for amodel that considers interband scattering in more detail. Anotherexample of a two-gap fit is shown with a local measurement ofpenetration depth in Ba (Fe0.95Co0.05)2As2 using magnetic forcemicroscopy and scanning SQUID spectroscopy, which observed atemperature dependence that varies about ten times more slowlythan in bulk measurements114. These data were well fitted witha fully gapped model with two different gaps, whereas the bulkmeasurement is not obviously consistent with a fully gapped modelunless disorder is considered.

Recent studies of the low-temperature electronic specific heat(γ ) have added important insights. In the BaFe2−xCoxAs2 system,a systematic study of the SC portion of γ as a function of x hasrevealed a lack of any strong doping dependence, signifying nomajor change in the gap structure through the superconductingrange of concentrations; the data of ref. 115 are fitted usinga two-gap model, yielding a factor-of-two ratio between gapamplitudes that does not vary by more than 10% through severalCo concentrations. The width of the SC transition at Tc, however,does show a significant increase away from optimal doping. Thismay be in line with the conclusions from thermal-conductivitymeasurements of weakened pairing strength away from optimaldoping108. A more intriguing find involves measurements of γin the T = 0 limit in Ba(Fe0.92Co0.08)2As2 (Tc = 20K; ref. 115)and BaFe2(As0.7P0.3)2 (Tc = 30K; ref. 116), both of which reporta sizeable residual contribution in the SC state that is ∼20%

of the estimated normal-state electronic contribution. However,subsequent studies have shown this residual contribution to beminimized at optimal doping in BaFe2−xCoxAs2 (ref. 117), andvanishingly small in Ba0.68K0.32Fe2As2 (refs 118,119), pointing to anorigin linked to sample homogeneity. Although unconventional,the field dependence of γ in both FeSC systems does notfollow the usual behaviour expected for nodal excitations, suchas the well-known H 1/2 dependence due to the Volovik effect.In Ba(Fe0.92Co0.08)2As2, a sublinear field dependence is indeedpresent but it cannot be fitted by a clean d-wave gap, and isbetter described by either a dirty d-wave or an anisotropic s-wave gap structure115. Likewise, in BaFe2(As0.7P0.3)2 (ref. 116) andBa0.6K0.4Fe2As2 (ref. 120) the observed linear field dependence ismore in line with a pairing symmetry that is isotropic on at leastone FS sheet that contributes significantly to the electronic densityof states (ref. 116). However, a recent calculation of the Volovikeffect for a two-band s-wave state with unequal gap sizes doessuggest that deviations from the usual square-root dependenceare not unexpected121.

A more provocative observation has to do with an unusualscaling of the jump in specific heat with Tc, as first identified inK-, Co- and Ni-doped BaFe2As2 systems122. Because the phononcontribution is difficult to estimate near Tc owing to elevatedtemperatures, it is not straightforward to extract the electronicnormal state γ at the transition and thus enable a comparison ofthe usual normalized ratio 1C(Tc)/γTc to the BCS expectationof 1.43. Instead, ref. 122 compared the absolute size of the jump,1C(Tc), and Tc values of several different samples and founda unique power-law scaling that seems to go as 1C(Tc) ∼ Tc

3.As shown in Fig. 3, a compilation of all data available for FeSCsystems so far confirms the initial observation to hold in subsequentmeasurements of K-doped118,119,123 and Co-doped115,124 BaFe2As2systems. Measurements in several other systems, including Rh-,Pd- (ref. 125) and Pt-doped12 BaFe2As2 materials, as well asFeTe0.85S0.15 (ref. 126), LaFePO (ref. 127), PrFePO (ref. 128),FeSe0.5Te0.5 (ref. 129) and LaFeAsO0.89F0.11 (ref. 130), also fallapproximately on the scaling plot. (Note that, so far, 1111-type FeSCs rarely show a large signature of their SC transitionsin specific heat, possibly due to sample quality, which maybe improved in the future.) Assuming that the enhancement1C(Tc) is purely electronic, this observation is difficult toexplain using BCS theory. According to ref. 131, it wouldrequire extremely unnatural fine-tuning of the pairing attractionto attain the proper scaling, leading to the conclusion thatthe underlying ground state is not a usual Fermi liquid butinstead is quantum critical. However, it has also been proposedthat strong pair-breaking can also result in such scaling132.These opposing views can potentially be explained throughcontrolled studies of specific heat and pair-breaking, the latterbeing discussed below.

First noted in the case of SrFe2−xCoxAs2 (ref. 10), it was quicklyrecognized that the act of chemical substitution directly into theactive pairing layer in the FeSCs presents a stunning contrast tothe well-known detrimental effect of Cu-plane disorder in thecuprates. Although there is a consensus that it is better (in thesense of attaining higher Tc values) to minimize disorder withinthe Fe planes, the mere fact that we can still attain a Tc valuenear 25K with strong disorder in the Fe plane (that is, by ∼10%substitution for Fe) presents a conundrum: how do we disentanglethe good (doping/SC optimization) from the bad (pair-breakingdisorder)? Pair-breaking studies are extremely useful for identifyinga sign-changing OP, where non-magnetic impurities should bestrong pair-breakers owing to the effect of a scattering event on themomentum-coupled OP phase. However, given the debate aboutthe effects of chemical substitution in FeSCs discussed earlier, itis not clear how any substitution within the active layer can be





considered to act only as an impurity scattering centre. Luckily,there are other methods of systematically inducing disorder. Forexample, alpha-particle irradiation was used to study pair-breakingin a controlledmanner by irradiating aNdFeAsO1−xFx single-crystalsample with Tc(0)=46K (ref. 133), resulting in a weak suppressionof Tc closely tied to irradiation-induced defects of a magneticnature. This is suggestive of a sign-changing OP. Penetration-depthmeasurements of Co- and Ni-doped BaFe2As2 as a function ofirradiation with Pb ions have also shown a ‘clean’ suppression ofTc with increasing defects, as well as a systematic suppression ofthe low-temperature power-law exponent of the penetration-depthtemperature dependence that is consistent with a nodeless s± stateaffected by pair-breaking scattering intermediate between Bornand unitary limits112.

Finally, results from other experiments provide further insightthat must be considered. Raman scattering is particularly usefulbecause it is capable of sampling specific regions of the BZ, henceprobing the momentum distribution of low-lying gap excitations.A Raman study on BaFe2−xCoxAs2 samples134 provides evidencefor a strong gap variation on the electron pockets consistent withthe anisotropic s± state discussed above. Muon spin-relaxationmeasurements of the penetration depth of optimally dopedBa(Fe0.926Co0.074)2As2 fit well to an isotropic two-gap structurewith one of the gaps being very small as compared with the BCSexpectation135. Last but not least, scanning tunnelling microscopyexperiments on BaFe2−xCoxAs2 have revealed an unusual gapstructure that does not strictly fit either a simple s- or d-waveshape, but also does not show any fourfold internal vortexstructure that would be expected in a d-wave case136. Such directmeasures of the superconducting OP symmetry will be importantfor future determination of the true variety of gap structuresin the FeSC materials.

Pairingmechanism, correlations and quantum criticalityFrom a general standpoint, the interplay of magnetism andsuperconductivity strongly suggests that magnetic fluctuationsare involved either directly or indirectly in the Cooper pairingin the FeSCs. In the context of magnetism, pairing couldarise from fluctuations emanating from a quantum criticalpoint, or an alternative pairing mechanism may simply benefitfrom the suppression of an antagonistic long-range magneticallyordered state, or a more complicated scenario involving theoptimal combination of three players — Coulomb repulsion,spin fluctuations and phonon coupling — may favour high-Tcsuperconductivity in these materials. First off, phonons alonewere quickly ruled out as a standalone contender for the pairingmediator. A calculation of electron–phonon coupling from firstprinciples helped to conclude that LaFeAsOF is intrinsically at mosta very poor electron–phonon superconductor (although includingthe effects of magnetism can increase the coupling constant byup to 50%; ref. 137). The classic isotope-effect experiment, whichprovided the first strong evidence for phonon-mediated Cooperpairing in conventional superconductors, is a well-known methodof probing the role of phonons (albeit not always conclusively evenfor conventional superconductors). One of the first studies didnot find any O isotope effect in SmFeAsO1−xFx, but did find asignificant Fe isotope effect (‘α’ exponent of ∼0.35) on both themagnetic and superconducting transitions in both SmFeAsO1−xFxand Ba1−xKxFe2As2 (ref. 138), suggesting that phonons are at leastintermediate players. However, subsequent studies on control- andisotope-substituted samples of both systems grown under identicalconditions report the absence of an appreciable isotope effect ineither case, motivating the need for further study139.

The strength of the electronic correlations in the iron-basedmaterials is an important issue that has received much theoreticaland experimental study. The present experiments show that a

modest level of correlations exists, but that the correlations arenot as strong as in the cuprates. A simple indication of this isthe absence of any clear Mott physics in the FeSCs: the parentcompounds are all clearly metallic, and there is no indication ofnearby insulating behaviour. However, conflicting opinions havebeen generated by experimental results. Optical measurementson LaFePO have indicated that many-body effects are important,identifying this material as a moderately correlated metal andBaFe2As2 as even more so140. In contrast, X-ray absorptionand inelastic scattering measurements on SmFeAsO0.85, BaFe2As2and LaFe2P2 show that their spectra closely resemble those ofelemental metallic Fe, thus arguing for weak correlations in thesematerials141 (although elemental Fe itself, with a Curie temperatureof over 1,000K, is not exactly an uncorrelated system!). Recentcalculations indicate that the correlated nature of the paramagneticstate gives rise to very fast-fluctuating moments142, providing apotential explanation for the reduced static moment size observedexperimentally. In the end, LaFePO may indeed have strongercorrelations than 1111- and 122-type FeSC materials, which couldexplain the observations of more unconventional (possibly d-wave)superconductivity in this system.

Regardless of the role of strong correlations, spin fluctuations,which possibly provide the collective spin-one excitation thatmediates pairing, are clearly abundant in the FeSCs. Consideringthe first-order nature of the SDW transitions in these systems,the fluctuations are surprisingly persistent up to fairly hightemperatures. For instance, the well-known increasing behaviourof magnetic susceptibility up to very high temperatures, so far auniversal feature of the FeSCs, is considered an indication of AFMfluctuations143. Also, Mossbauer spectroscopy of BaFe2−xCoxAs2has observed a magnetic hyperfine component consistent withshort-range AFM correlations at temperatures up to 1.5 × TN(ref. 144), and neutron-scattering studies of CaFe2As2 provideevidence for 2D spin fluctuations that persist up to 1.8 × TN(ref. 145) — all despite the first-order nature of both magnetic andstructural transitions in these systems.

An NMR study of normal-state spin dynamics in BaFe2−xCoxAs2has shown that the uniform spin susceptibility is systematically sup-pressed with increasing Co concentration, with superconductivityoptimized near a quantum critical point where SDW order spinfluctuations are maximal146. This was suggested to be controlledby the suppression of inter-band transitions (that is, disappear-ance of a hole pocket) that weakens the nesting condition49, andit is indeed true that dHvA oscillations observed in the relatedP-doped BaFe2As2 system show a substantial shrinking of electronpockets and strong mass enhancement on approach to the mag-netic/superconducting boundary at optimalTc (ref. 32). Because themeasured Fermi surfaces in the P-doped series are inconsistent withan estimated (extrapolated) smooth progression between P andAs end-members, it was concluded in ref. 32 that spin fluctuationsare the likely explanation for band structure changes, and conse-quentially superconductivity.

With good ties between superconductivity and spin fluctuationsfrom the suppression of magnetic order, it is fair to say thatquantum criticality may play an important role. Calculationsindeed suggest a competition between electron localization anditinerancy, which should yield fertile soil for quantum criticality147,and the observed specific heat scaling as noted above mayprovide strong evidence for a truly non-Fermi-liquid groundstate131. However, experimentally there is surprisingly little evidencefor strong deviations from Fermi-liquid behaviour, especiallyas compared with other quantum critical systems such as thecuprates and heavy-fermion materials. For example, althoughT -linear resistivity is indeed rampant throughout the optimallydoped FeSCs, disentanglement of electron and hole carriers(with some assumptions) has enabled transport measurements





NATURE PHYSICS DOI: 10.1038/NPHYS1759 REVIEW ARTICLEof BaFe2−xCoxAs2 to be interpreted as consistent with Fermi-liquid expectations46. More importantly, strong evidence for aFermi-liquid ground state in BaFe2As2−xPx is provided directlyby the observation of quantum oscillations throughout its phasediagram32, even though this system’s normal state above Tc showstell-tale signatures of a quantum critical point near x = 0.66(ref. 148). Because transport measurements near optimal dopingare limited to temperatures above Tc, it will be an experimentaltask to develop methods of probing the low-temperature groundstate either indirectly in SC systems, or by studying related low-Tcor non-SC materials that can be tuned to criticality, to explainthe true ground-state properties near the demise of AFM order.Recent progress has been made to this effect, for instance inCu-doped BaFe2As2 (ref. 15) and P-doped CeFeAsO (ref. 72), bothof which show complete suppression of magnetic order in theabsence of any SC phase.

With difficulties in probing the underlying ground state nearthe quantum critical point, studies of the coexistence region ofsuperconductivity and antiferromagnetism are among the mostimportant ongoing efforts. Muon spin-resonance experiments haveshown contrasting pictures regarding the level of coexistence, witha complete separation of AFM and SC phases shown in stud-ies of La- and Ce-based 1111-type materials5 and coexistence ofdisordered but static magnetism and superconductivity in Sm-FeAsOF with possible phase separation6. In the 122-type mate-rials, mesoscopic phase separation into magnetic and paramag-netic (superconducting) regions has been shown in Ba1−xKxFe2As2,Sr1−xNaxFe2As2 and CaFe2As2 under pressure149. If experimentscan show that microscopic coexistence of AFM and SC is in-deed intrinsic to FeSC systems, then the competition of thesetwo ground states is not surprising in a scenario where Cooperpairing is mediated by strong fluctuations of AFM order. Thisis indeed the case in the Ce-based 115-type materials, wherethe same f -electron states are known to be responsible for bothAFM and SC. A recent report150 of ‘atomic’ coexistence of SCand AFM order on each Fe site is a thought-provoking ob-servation that speaks to the level at which these two states ofmatter can cohabitate.

ConclusionsProgress in understanding superconductivity in iron-based ma-terials has advanced tremendously over the past year thanks toabundant theoretical and experimental efforts. Considering thatthere is overall good agreement between many different experi-ments on the general properties of these materials, we can safelyconclude that the chemistry is under sufficient control to allowfor reasonable comparisons of experimental data without majorconcerns about sample quality variations. This is one of themain reasons why, after only two years, we have an extensiveand reliable set of thermodynamic, transport, surface and spec-troscopic data with which to analyse the general and universalproperties of this new breed of superconductors. It is also thereason why the observed diversity of properties, especially of theSC state, is so puzzling: the intrinsic nature of these materialsseems to include a strong sensitivity to many real and unavoid-able perturbations, which yields diverse yet reproducible results.Theoretically, this may be due to a near degeneracy in energy ofdifferent extended s-wave and even d-wave OP symmetry states,implying a sensitivity of gap symmetry to everything from dis-order to lattice density. Overall, it is likely that a generic rep-resentative OP symmetry will involve a sign-changing structurewith one fairly isotropic gap and another gap with at least deepminima, and more probably with accidental nodes. In particular,the presence of anisotropic and multiband scattering, and strongc-axis dispersion of at least parts of the FS structure, will makeit difficult to conclude on any particular universal gap structure.

However, phase-sensitive experiments will help to pin down anintrinsic symmetry, and controlled experiments designed to probethe accidental nature of nodes may provide a better understand-ing of their dependence on tunable experimental quantities. Inthe end, these may be moot points, as the relatively high Tcvalues of the iron-based superconductors do not seem to caremuch about such details.

Finally, this brief review article cannot hope to cover all ofthe ongoing research in such an active and rapidly developingfield as the iron-based superconductors. For example, the possiblerole of more exotic physics, such as nematic order, has notbeen discussed. Also, the physics and experiments related topossible applications of these materials, especially those involvingthe significantly high values of upper critical fields of theorder of 50 T and critical currents exceeding 106 A cm−2, havebeen omitted. The research on the FeSCs has already led tonew insights into the novel physics of correlated electronicmaterials, but there is still much to learn. If the cause ofthe high-temperature superconductivity in these materials canbe understood at the level that conventional electron–phononsuperconductors are understood, then it is possible that room-temperature superconductivity may prove feasible. Even if thiselusive goal is not achieved, the future research on iron-basedsystems will lead to more knowledge of materials with exoticcondensed-matter-physics properties. As has already been shownby the iron-based superconductors, the cuprates, the organics andthe heavy fermions, superconductivity and magnetism are not asincompatible as was once believed.

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AcknowledgementsThe authors would like to thank P. J. Hirschfeld, J. W. Lynn, I. I. Mazin, D. J. Scalapinoand L. Taillefer for discussions and comments. This research was supported byAFOSR-MURI under FA9550-09-1-0603.

Additional informationThe authors declare no competing financial interests. Reprints and permissionsinformation is available online at http://npg.nature.com/reprintsandpermissions.Correspondence and requests for materials should be addressed to J.P.





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