Superconductivity in Ab initio Low-Energy Effective Model for Iron-Based Superconductor

To clarify microscopic mechanism of superconductivity in iron-based superconductors, we study the {\it ab initio} low-energy effective models for iron-based superconductor~[1], particularly for LaFeAsO by using multi-variable variational Monte Carlo (mVMC) method, which properly takes into account both spatial and dynamical quantum fluctuations. The calculated magnetic order was shown to correctly reproduce the experimental material dependences~[2,3]. By extending these normal state studies, we find that superconductivity emerges in the electron doped LaFeAsO in essential agreement with the experimental results. The pairing satisfies $s\pm$ symmetry. We discuss the role of antiferromagnetic correlations, Mott proximity, and charge and orbital fluctuations in stabilizing the superconductivity. The specific orbital ($d_{X^2-Y^2}$) is shown to play a role of orbital-selected doped Mott insulator in stabilizing the superconducting phase as well as the antiferromagnetic phase. We discuss similarity and dissimilarity to the cuprate superconductors. ~[1]~T. Miyake $et$ $al$., J. Phys. Soc. Jpn. {\bf 79}, 044705 (2010). ~[2]~T. Misawa $et$ $al$., J. Phys. Soc. Jpn. {\bf 80}, 023704 (2011). ~[3]~T. Misawa $et$ $al$., Phys. Rev. Lett. {\bf 108}, 177007 (2012).