Pairing Mechanism In Alkaline Iron Selenide Superconductors

An important issue in various iron-based superconductors is whether electrons are itinerant or localized. Theories in the itinerant picture (IP) use the Hubbard model as the starting point. The local Coulomb interaction, Hund’s rule coupling and the quasi-nesting between electron and hole pockets lead to strong spin fluctuation (SF). The pairing interaction is induced by the overlap between superconducting and magnetic channels. As long as the SF is not strong enough to form magnetic order, superconduc-tivity (SC) emerges instead at low temperature via the Cooper Mechanism. Together with the local interactions, the topology of the Fermi surfaces and the underlying band structure determine the leading SF that drives pairing in a specific symmetry channel. In the local-moment picture (LP), the interactions are composed of the spin exchange coupling on nearest-neighbor (NN) and next-nearest-neighbor (NNN) bonds in the so-called t-J1-J2model. In this picture, the pairing interaction is already provided by the exchange coupling at the mean-field level. The competition between the two ex-change couplings determines the pairing amplitudes on the NN and NNN bonds. The pairing symmetry is determined by maximizing the resulting gap function on the Fermi surfaces. For samples with both hole and electron pockets, the results from both pic-tures are qualitatively consistent with experiments. In the IP, the SF-driven repulsive pair-hopping interaction between hole and electron pockets forces the gap function to change sign, forming the so-called s±pairing. In the LP, when J2on NNN bonds dom-inates over J1on NN bonds, pairing occurs primarily on NNN bonds and the matching to the Fermi surface topology results in the s±-wave symmetry. However, in the recent-ly discovered alkaline iron-selenide superconductors AFe2Se2(AFS), there appears to be an inconsistency between the two pictures. In the IP, functional renormalization group (FRG) calculations based on five-band models found that the inter-pocket scat-tering between two electron pockets dominates, leading to strong checkerboard-type SF. As a result, a nodeless d-wave pairing emerges as the leading pairing symmetry. In the LP, the pairing symmetry remains to be s-wave, as long as J2dominates over J1In Chap. I, it is introduced of the brief history of superconductivity and the de-velopment of iron-based superconductors. In Chap. II, we study the Hubbard mod-el with the method of singlet-mode FRG(SMFRG) in itinerant picture(IP). The SF is determined by the band structure. As we increase t1, the hole-pocket at Γ point is pushed down, which restrains the SF leaded by electron-hole scattering. As a result, the intra-pocket scattering in electron pocket dominates. In this case, the paring symmetry changes from s-wave to d-wave. In Chap. Ⅲ, we apply the slave-boson meanfield the-ory(SBMF) to study the t-J model in local picture(LP). As we increase t1, the magnetic order changes from stripe-type to checkerboard-type. The pairing symmetry is also changes from s-wave to d-wave, which is consistent with the results of SMFRG qual-itatively. In Chap. IV, we conclude the essay with phase diagrams of two pictures and the results are qualitatively consistent. The pairing symmetry of alkaline iron selenide superconductors is s-wave.