Iron-based superconductors pose the central open mechanism question of the field: what interaction glues the Cooper pairs? Their parent compounds are metals with coherent quasiparticles rather than doped Mott insulators, yet they order antiferromagnetically with sizable local moments, and their superconducting states show a neutron spin resonance near twice the gap energy with magnetic fluctuations persisting through the superconducting transition. This problem asks for the microscopic origin of the magnetic pairing interaction: is it generated by spin fluctuations of the itinerant electrons themselves (the weak-coupling Berk-Schrieffer route to the sign-changing s±s_\pm gap), by local-moment physics (superexchange and resonating-valence-bond correlations), or by a correlated hybrid of the two, and how does that mechanism produce the observed gap symmetry, gap structure, and pairing temperatures from a metallic normal state. The problem remains open: reviews from both theoretical schools through 2021 and new pairing proposals through 2025 describe the glue's origin as unresolved, and existing experiments constrain the gap symmetry without discriminating the glue's microscopic origin.

Background

Superconductivity near 26 K in LaFeAsO1−x_{1-x}Fx_x (2008), later raised to about 55 K in related compounds and to 60-100 K in monolayer FeSe films, defines the second known family of high-temperature superconductors: layered iron pnictides (e.g., the 122-family compound BaFe2_2As2_2) and chalcogenides (e.g., FeSe), whose low-energy electrons occupy five Fe 3dd orbitals forming several hole pockets around the Brillouin-zone center and electron pockets at the zone corner. Unlike the cuprates, whose parent compounds are Mott insulators (electrons localized by Coulomb repulsion), the undoped iron compounds are metals: angle-resolved photoemission (ARPES, which maps the band structure by ejecting electrons with ultraviolet light) and quantum oscillations (periodic oscillations of resistivity or magnetization in a magnetic field, which resolve the Fermi surface) observe coherent quasiparticle bands crossing the Fermi level. At the same time they develop stripelike antiferromagnetic order on cooling, with ordered moments per Fe far below the free-ion value but with sizable fluctuating moments, and dynamical magnetic correlations that survive into the superconducting state.

Two competing frameworks for the pairing mechanism grew out of this dual character. In the itinerant picture, the pairing glue is the collective spin fluctuation of the metallic electrons themselves: extending Berk and Schrieffer's 1966 observation that repulsive spin fluctuations of a metal can generate an effective attraction, Mazin, Singh, Johannes, and Du proposed that repulsive interband pair scattering between hole and electron pockets favors a sign-changing s-wave state, the s±s_\pm state, in which the superconducting gap has opposite signs on the two pocket sets; Kuroki and co-workers derived the same conclusion from random-phase-approximation calculations (a weak-coupling scheme that sums particle-hole fluctuation diagrams). In the local-moment picture, descending from the resonating valence bond (RVB) idea used for the cuprates, the relevant degrees of freedom are more strongly coupled local spins connected by antiferromagnetic exchange couplings J1J_1 and J2J_2 between nearest and next-nearest Fe neighbors, whose geometric frustration shapes both magnetism and superconductivity; Si and Abrahams emphasized this strongly correlated, frustrated regime, and You and Weng's book chapter formulated a hybrid theory in which itinerant quasiparticles and local moments coexist as emergent, weakly interpenetrating subsystems, with pairing of the itinerant electrons mediated by fluctuations of the local moments.

Several experimental facts anchor the debate. Inelastic neutron scattering observes in the superconducting state a magnetic resonance mode at an energy near twice the superconducting gap energy, 2Δ2\Delta, a hallmark consistent with a sign-changing gap (the resonance is the spin exciton created when the sign reversal opens a decay channel); the same measurements show magnetic spectral weight persisting well above the superconducting transition temperature, and spin-wave measurements on parent and related compounds extract exchange energies of order tens of meV, i.e., a scale comparable to the pairing energy. On the theory side, dynamical mean-field theory (DMFT, a method treating local quantum fluctuations exactly within a self-consistent bath) describes the normal state as a moderately correlated Hund metal, in which Hund's-rule coupling (the intra-atomic exchange favoring aligned Fe 3dd spins) suppresses quasiparticle coherence without destroying it, so that coherent itinerant carriers and sizeable local moments coexist. This softens the strict itinerant-versus-local dichotomy but deepens the mechanism question: in such an intermediate-correlation regime neither weak-coupling nor strong-coupling theory is controlled, and the identity of the dominant pairing interaction remains undetermined.

Problem Statement

Determine the microscopic origin of the magnetic pairing glue in iron-based superconductors. Specifically: is the pairing interaction between electrons generated by spin fluctuations of the itinerant quasiparticles themselves (the Berk-Schrieffer weak-coupling route to the sign-changing s±s_\pm gap), by the physics of more strongly coupled local moments (superexchange and resonating-valence-bond correlations in the J1J_1-J2J_2 or hybrid itinerant-local-moment descriptions), or by a specified correlated combination of the two, and how does the resulting mechanism account, from the metallic normal state of the parent compounds, for the observed gap symmetry and momentum-resolved gap structures — the sign-changing s±s_\pm symmetry where it is established — and for the pairing temperatures across the iron-based families? A resolution requires identifying the dominant origin of the pairing glue among these possibilities and demonstrating that the resulting mechanism accounts for the observed gap symmetry and momentum-resolved gap structure and for the pairing temperatures across the iron-based families; identifying a candidate mechanism without showing that it reproduces these observations does not resolve the task.

References

  1. Yi-Zhuang You and Zheng-Yu Weng, "Coexisting Itinerant and Localized Electrons in Iron-Based Superconductors" (book chapter, 2013), arXiv:1311.4094, https://arxiv.org/abs/1311.4094
  2. N. F. Berk and J. R. Schrieffer, "Effect of Ferromagnetic Spin Correlations on Superconductivity", Phys. Rev. Lett. 17, 433 (1966), DOI 10.1103/PhysRevLett.17.433, https://doi.org/10.1103/PhysRevLett.17.433
  3. I. I. Mazin, D. J. Singh, M. D. Johannes, and M. H. Du, "Unconventional superconductivity with a sign reversal in the order parameter of LaFeAsO1−x_{1-x}Fx_x", Phys. Rev. Lett. 101, 057003 (2008), DOI 10.1103/PhysRevLett.101.057003, https://doi.org/10.1103/PhysRevLett.101.057003
  4. Kazuhiko Kuroki, Seiichiro Onari, Ryotaro Arita, Hidetomo Usui, Yukio Tanaka, Hiroshi Kontani, and Hideo Aoki, "Unconventional pairing originating from disconnected Fermi surfaces in the iron-based superconductor", New J. Phys. 11, 025017 (2009), DOI 10.1088/1367-2630-11/2/025017, https://doi.org/10.1088/1367-2630-11/2/025017
  5. Qimiao Si and Elihu Abrahams, "Strong correlations and magnetic frustration in the high-Tc iron pnictides", Phys. Rev. Lett. 101, 076401 (2008), DOI 10.1103/PhysRevLett.101.076401, https://doi.org/10.1103/PhysRevLett.101.076401
  6. Jun Zhao, D. T. Adroja, Dao-Xin Yao, R. Bewley, Shiliang Li, X. F. Wang, G. Wu, X. H. Chen, Jiangping Hu, and Pengcheng Dai, "Spin waves and magnetic exchange interactions in CaFe2As2", Nat. Phys. 5, 555-560 (2009), DOI 10.1038/nphys1336, https://doi.org/10.1038/nphys1336
  7. Hiroshi Kontani and Seiichiro Onari, "Orbital-Fluctuation-Mediated Superconductivity in Iron Pnictides: Analysis of the Five-Orbital Hubbard-Holstein Model", Phys. Rev. Lett. 104, 157001 (2010), DOI 10.1103/PhysRevLett.104.157001, https://doi.org/10.1103/PhysRevLett.104.157001
  8. M. D. Lumsden and A. D. Christianson, "Magnetism in Fe-based superconductors", J. Phys.: Condens. Matter 22, 203203 (2010), DOI 10.1088/0953-8984/22/20/203203, https://doi.org/10.1088/0953-8984/22/20/203203
  9. Z. P. Yin, K. Haule, and G. Kotliar, "Kinetic frustration and the nature of the magnetic and paramagnetic states in iron pnictides and iron chalcogenides", Nat. Mater. 10, 932-935 (2011), DOI 10.1038/nmat3120, https://doi.org/10.1038/nmat3120
  10. Miaoyin Wang, Chen Fang, Dao-Xin Yao, GuoTai Tan, Leland W. Harriger, Yu Song, Tucker Netherton, Chenglin Zhang, Meng Wang, Matthew B. Stone, Wei Tian, Jiangping Hu, and Pengcheng Dai, "Spin waves and magnetic exchange interactions in insulating Rb0.89Fe1.58Se2", Nat. Commun. 2, 580 (2011), DOI 10.1038/ncomms1573, https://doi.org/10.1038/ncomms1573
  11. Qimiao Si, Rong Yu, and Elihu Abrahams, "High-temperature superconductivity in iron pnictides and chalcogenides", Nat. Rev. Mater. 1, 16017 (2016), DOI 10.1038/natrevmats.2016.17, https://doi.org/10.1038/natrevmats.2016.17
  12. Peter J. Hirschfeld, "Using gap symmetry and structure to reveal the pairing mechanism in Fe-based superconductors", C. R. Physique 17, 197-231 (2016), DOI 10.1016/j.crhy.2015.10.002, https://doi.org/10.1016/j.crhy.2015.10.002
  13. P. O. Sprau, A. Kostin, A. Kreisel, A. E. Böhmer, V. Taufour, P. C. Canfield, S. Mukherjee, P. J. Hirschfeld, B. M. Andersen, and J. C. Séamus Davis, "Discovery of orbital-selective Cooper pairing in FeSe", Science 357, 75-82 (2017), DOI 10.1126/science.aal1575, https://doi.org/10.1126/science.aal1575
  14. Anna E. Böhmer and Andreas Kreisel, "Nematicity, magnetism and superconductivity in FeSe", J. Phys.: Condens. Matter 30, 023001 (2018), DOI 10.1088/1361-648X/aa9caa, https://doi.org/10.1088/1361-648X/aa9caa
  15. Rong Yu, Haoyu Hu, Emilian M. Nica, Jian-Xin Zhu, and Qimiao Si, "Orbital Selectivity in Electron Correlations and Superconducting Pairing of Iron-Based Superconductors", Front. Phys. 9, 578347 (2021), DOI 10.3389/fphy.2021.578347, https://doi.org/10.3389/fphy.2021.578347
  16. Yashar Komijani, Elio König, and Piers Coleman, "Triplet pairing, orbital selectivity, and correlations in iron-based superconductors", Phys. Rev. B 112, 125120 (2025), arXiv:2302.09702, DOI 10.1103/nx2p-k972, https://doi.org/10.1103/nx2p-k972