The past is prologue

Iron-based high-temperature superconductors were discovered in January 2008, and they

have arguably been the biggest news in the field of superconductivity since the

appearance of the cuprate superconductors in the late eighties [1]. Although the

cuprates demonstrated that high-temperature superconductivity was possible, the iron

-based materials prove that this phenomenon is not limited to a single class of

compounds.

So far, the story unraveling about the new iron-based superconductors has been quite

rewarding for practitioners. In order to appreciate the relevant timescales, remember

that for the cuprates, nearly ten years passed before a general consensus was reached

on the pairing symmetry, and consider that there still is no agreement on the

underlying mechanism. More in line with the story of superconductivity in MgB2, where

full consensus was achieved within a year, a plausible model was proposed within

weeks after the discovery of iron-based superconductors [2] and gained support from

the majority of researchers in the field. In this model, the calculated and

experimentally confirmed [1] electronic band structure of iron-based superconductors

is semimetallic, consisting of hole and electron Fermi surface pockets, separated by

a (π,π) wave vector in momentum space (see Fig. 1). This suggests the existence of

a spin excitation with the same wave vector, which was indeed found experimentally

[3]. If one considers this spin excitation to be the pairing agent for

superconductivity [1], the resulting order parameters for the holes and for the

electrons will have opposite signs, with the overall angular momentum being L=0 (s-

type); hence the name s±.Early surprises and progress

This simple concept has been questioned on at least two occasions when new iron-based

superconducting materials were discovered. This happened first when two low-Tc

compounds, KFe2As2 and LaFePO, exhibited clear signs of gap nodes [4], which are not

required by symmetry in the s± model. Theoretically, this could still be

rationalized within an s± spin-fluctuation-induced superconductivity model. Indeed,

if there are other competing interactions, e.g., with phonons, or a particularly

strong Coulomb repulsion, a compromise can be found that results in gap nodes.

However, this point of view is substantially based on the fact that both KFe2As2 and

LaFePO have rather low critical temperatures. So, when a third compound was found

clearly exhibiting nodes, this explanation was severely shaken; the compound in

question was phosphorus-doped BaFe2As2, with Tc in excess of 30 K  [4].

Numerous model calculations appeared then, in which the combination of the angular

dependence of the orbital character of electronic bands and a strong Coulomb

repulsion led to patches of the “wrong” sign of the order parameter, and thus to

nodes [5]. Of course, whether this regime is realized or not depends on the material

in question; it is quite normal that some compounds are in the “nodal” region in

the parameter space, while others are not. This explanation, though it seems natural,

is not without problems: Retardation effects (different energy scales for the

superconducting pairing and the static electronic interactions) cause a

renormalization of the Coulomb repulsion; it becomes much less important than that

appearing in the static calculation, if not negligible. Most importantly, such

calculations yield strongly anisotropic gaps in all compounds, whether nodal or not.

However, angle-resolved photoemission spectroscopy (ARPES) shows uniform gaps

wherever it can map the electronic Fermi surface. Yet there was a feeling in the

community that even though our favorite model may have some quantitative issues, it

was conceptually correct, and had all the necessary potential to overcome its

problems; the quantitative details would eventually be ironed out.

Once again, doubt was cast on this model when another compound was found, Sr2VO3FeAs 

[6], which according to band structure calculations featured vanadium electrons at

the Fermi surface in addition to electrons and holes from iron, completely destroying

the neat dichotomy of the Fermi surfaces into well-separated electron and hole

pockets. However, it was soon discovered that the vanadium electrons, unlike the iron

ones, are strongly correlated in this system, and thus are completely removed from

the Fermi level [7]. This, of course, saves the model.

Thus, barring a few dissenters, towards the end of 2010 there was a general consensus

that even if the s± model may have problems with some measurements, compared to

alternatives it accounts for the entire body of the experiments in a much better way.