The 2008 discovery of superconductivity at Tc=26T_c = 26 K in fluorine-doped La[O1−x_{1-x}Fx_x]FeAs by Kamihara, Watanabe, Hirano and Hosono launched the iron-based superconductor family, the second material class with high superconducting transition temperatures after the cuprates. The discovery paper and the immediately surrounding literature posed a bundle of open questions: the origin of the ~150 K resistivity/susceptibility anomaly in the parent compound LaOFeAs, the origin of the low-temperature resistivity minimum and its suppression by fluorine doping, the reason for the unexpectedly high TcT_c (the pairing mechanism), and the relation of the superconducting phase to nearby magnetism, including a suggested proximity to ferromagnetism. Neutron diffraction, Moessbauer spectroscopy, NMR and systematic doping studies resolved the first, second and fourth questions: the ~150 K anomaly is a coupled tetragonal-to-orthorhombic structural transition followed by stripe-type antiferromagnetic spin-density-wave order at about 134-140 K with a small Fe moment, which fluorine doping suppresses in favor of a superconducting dome adjacent to the antiferromagnetic phase - antiferromagnetic, not ferromagnetic, proximity. What remains open is the microscopic pairing mechanism: what interaction pairs the electrons in La[O1−x_{1-x}Fx_x]FeAs and quantitatively sets Tc=26T_c = 26 K, and what exact role the antiferromagnetic, orbital and nematic fluctuations of the suppressed parent-state order play in the pairing. The leading candidate, a sign-changing s-wave (s±s_{\pm}) state mediated by antiferromagnetic spin fluctuations, is supported by neutron-resonance and NMR evidence but remains contested against orbital-fluctuation, s++s_{++}, nodal and d-wave scenarios; the most recent comprehensive review (2026) concludes that no single microscopic framework accounts for the iron-based superconductors.

Background

Superconductivity at high temperature was for two decades the exclusive property of the layered copper oxides (cuprates), where superconductivity emerges when carriers are doped into an antiferromagnetic parent compound and is widely believed to be mediated by antiferromagnetic spin fluctuations. In February 2008 Kamihara, Watanabe, Hirano and Hosono reported that the layered quaternary iron arsenide LaOFeAs - an oxypnictide (an oxide containing a pnictogen, here arsenic) with the tetragonal ZrCuSiAs-type structure of alternating La-O and Fe-As layers, often called the 1111 structure - becomes superconducting at TcT_c up to about 26 K when O2−O^{2-} is partially replaced by F−F^{-}, which donates electrons to the FeAs layers, with the highest TcT_c near x=0.11x = 0.11. Within months, applied pressure raised TcT_c to 43 K in the same compound and rare-earth substitution (Sm, Nd, Pr) pushed it above 50 K, establishing the iron pnictides as the second high-TcT_c family. The undoped parent compound LaOFeAs, however, is a non-superconducting metal that shows an anomaly near 150 K in both resistivity and dc magnetic susceptibility, and its resistivity passes through a low-temperature minimum before turning up at lower temperature; these normal-state anomalies fade as fluorine doping induces superconductivity. The discovery paper therefore posed the questions of what causes the 150 K anomaly, why doping suppresses it, what mechanism produces the unexpectedly high TcT_c, and how the superconducting phase relates to nearby magnetic tendencies - a proximity to ferromagnetism having been suggested in the immediately following work of the same group and in density-functional calculations that found LaFeAsO near competing ferromagnetic and antiferromagnetic instabilities. Later work answered the first two questions directly. Neutron diffraction (de la Cruz et al., 2008) showed that LaOFeAs distorts structurally just below 155 K (from tetragonal P4/nmm to a lower-symmetry cell) and orders at about 134-137 K into a stripe-type antiferromagnetic spin-density wave (SDW - a periodic modulation of the electron spin density that gaps nested portions of the Fermi surface, the set of electronic states at the highest occupied energy in momentum space) with a small ordered moment of about 0.36 μB\mu_B per Fe; the ~150 K resistivity anomaly coincides with this coupled structural and magnetic transition, and fluorine doping suppresses both in favor of superconductivity. Moessbauer spectroscopy (Kitao et al., 2008) - a nuclear gamma-ray resonance probe of the magnetic field at the Fe nucleus - nuclear magnetic resonance (NMR; Nakai et al., 2012) and complete doping-dependent phase diagrams (Kondrat et al., 2009) confirmed this picture: the low-temperature resistivity upturn of the parent and lightly doped samples is a vestige of the SDW-gapped, carrier-localized state, and it disappears where the superconducting dome reaches its maximum. The magnetism neighboring the superconducting dome is thus stripe antiferromagnetism, not ferromagnetism. What remains unresolved is the pairing mechanism. Two 2008 theory papers (Mazin, Singh, Johannes and Du; Kuroki et al.) proposed that repulsive interband interactions mediated by the antiferromagnetic spin fluctuations of the multiband Fe 3d electronic structure produce a sign-changing extended s-wave state, called s±s_{\pm} (the superconducting order parameter reverses sign between the hole pockets at the Γ\Gamma point and the electron pockets at the M point, the standard high-symmetry points of the Brillouin zone of the square Fe-As lattice). Supporting evidence includes the absence of a Hebel-Slichter coherence peak (an enhancement of the nuclear spin-lattice relaxation rate just below TcT_c that is a hallmark of conventional sign-preserving s-wave pairing) and a T3T^3 nuclear spin-lattice relaxation rate in the superconducting state, and the neutron spin resonance - a collective magnetic excitation that appears below TcT_c at the nesting wavevector - whose momentum structure implies sign-changing gaps. However, the field has not converged: orbital-fluctuation pairing, robust non-sign-changing s++s_{++} states, nodal and d-wave states, electronic nematicity (spontaneous breaking of the tetragonal fourfold rotational symmetry at a temperature TST_S above the antiferromagnetic ordering temperature TNT_N, intertwined with the SDW and with orbital order), and sizable correlations driven by Hund's rule (the intra-atomic exchange coupling between the Fe 3d electrons) all remain live alternatives in different compounds, and quantitative accounts of the magnitude of TcT_c are lacking. Comprehensive reviews in 2010-2016 and the most recent review in 2026 state that the pairing mechanism of the iron-based superconductors remains without a single accepted microscopic framework.

Problem Statement

Identify the microscopic mechanism by which electrons are paired in the fluorine-doped layered iron arsenide La[O1−x_{1-x}Fx_x]FeAs, which superconducts at TcT_c up to about 26 K near x=0.11x = 0.11, and establish it quantitatively. The target is, jointly, to: (i) identify the interaction responsible for the pairing - antiferromagnetic spin fluctuations inherited from the suppressed stripe spin-density-wave order of the parent compound, competing ferromagnetic or orbital fluctuations, nematic fluctuations, correlation effects, or a combination - with its momentum and orbital structure; (ii) show that this interaction reproduces the observed superconducting dome of the LaFeAsO1−x_{1-x}Fx_x phase diagram, including the magnitude of TcT_c and its doping dependence, and the superconducting gap structure (gap sizes, anisotropy, sign changes between Fermi-surface sheets, and nodal or nodeless character) measured by spectroscopic, thermodynamic and transport probes; and (iii) state what role, if any, the proximity of the superconducting phase to the antiferromagnetic, orbital and nematic order of the parent compound plays in the pairing - that is, the mechanistic part of the question posed at the discovery of this superconductor. The two other open issues raised at the discovery - the origin of the ~150 K resistivity anomaly of undoped LaOFeAs and of the low-temperature resistivity minimum, and their suppression by fluorine doping - have been resolved (coupled structural and stripe-antiferromagnetic spin-density-wave transitions) and are not part of this problem, except insofar as the fluctuation background they define feeds the pairing interaction. No specific gap symmetry, pairing channel, theoretical framework or experimental method is prescribed; the target is a demonstrated microscopic mechanism, established quantitatively: naming the pairing interaction and showing quantitative agreement of the resulting TcT_c, its doping dependence and the gap structure with the measured LaFeAsO1−x_{1-x}Fx_x data.

References

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