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The ground state of K$_{0.8+x}$Fe$_{1.6+y}$Se$_2$ and other iron-basedselenide superconductors are doped antiferromagnetic semiconductors. There arewell defined iron local moments whose energies are separated from those ofconduction electrons by a large band gap in these materials. We propose thatthe low energy physics of this system is governed by a model Hamiltonian ofinteracting electrons with on-site ferromagnetic exchange interactions andinter-site superexchange interactions. We have derived the effective pairingpotential of electrons under the linear spin-wave approximation and shown thatthe superconductivity can be driven by mediating coherent spin wave excitationsin these materials. Our work provides a natural account for the coexistence ofsuperconducting and antiferromagnetic long range orders observed by neutronscattering and other experiments.

Superconductivity mediated by the antiferromagnetic spin-wave in chalcogenide iron-base superconductors