We theoretically investigate the coexistence of antiferromagnetism and superconductivity in the iron-based superconductors by using the mean-field theory for two-and three-orbital models. We find that both the s+−-wave and s++-wave superconductivity can coexist with antiferromagnetism in the two models. On Dirac Fermi surfaces emerging in the antiferromagnetic phase, a superconducting-gap function has a node for s++ wave but is nodeless for s+− wave. On the other hand, the gap function on non-Dirac Fermi surfaces is either nodeless or accidentally nodal, depending on the parameters of pairing interaction, which is independent of pairing symmetry.
IntroductionUnderstanding the phase diagram of iron-based superconductors is a key to clarify the physics of superconductivity of these systems. Parent compounds of iron-based superconductors show an antiferromagnetic (AFM) spin density wave (SDW) below a Néel temperature. With hole or electron doping, magnetization is suppressed and superconductivity emerges. A close relationship of AFM and superconducting (SC) phases indicates that the formation of a Cooper pair is mediated by spin fluctuation, which leads to s +− -wave order 1, 2 where the sign of the gap function on hole Fermi surfaces (FSs) centered at the momentum k = (0, 0) is opposite to that on electron FSs at k=(π,0) and (0,π). On the other hand, it has been proposed that s ++ -wave order, where the two signs are the same, emerges when orbital fluctuation is responsible for superconductivity. 3, 4 s +− and s ++ are possible candidates of SC symmetry in iron-based superconductors.Since the AFM and SC phases are next to each other, the boundary of the two phases may provide useful information on superconductivity of iron-based superconductors. Intriguingly, Ba 1−x K x Fe 2 As 2 , Ba(Fe 1−x Co x ) 2 As 2 and BaFe 2 (As 1−x P x ) 2 show a microscopically coexisting phase of AFM and SC orders, supported by neutron diffraction, 5, 6 X-ray diffraction, 5, 7-9 and NMR 10, 11 experiments.Such a coexistence phase has theoretically been investigated, 12-17 where it is commonly assumed that FSs in a paramagnetic phase consists of a near-circular hole pocket centered at k = (0, 0) and an elliptical electron pocket at k=(π,0) and (0,π). The AFM order with wave vector Q=(π,0) mixes the hole and electron dispersions and a SDW gap is open. Resulting reconstructed FS is completely different from the FS of original paramagnetic phase. In the coexistence phase, it has been pointed out that the SC-gap function on the newly reconstructed