Orbital fluctuation theory in iron-based superconductors: s-wave superconductivity, structure transition, and impurity-induced nematic order

The main features in iron-based superconductors would be (i) the orthorhombic transition accompanied by remarkable softening of shear modulus, (ii) high-Tc superconductivity close to the orthorhombic phase, and (iii) nematic transition in the tetragonal phase. In this paper, we present a unified explanation for them, based on the orbital fluctuation theory, considering both the e-ph and the Coulomb interaction. It is found that a small e-ph coupling constant ($\lambda ~ 0.2$) is enough to produce large orbital (=charge quadrupole $O_{xz/yz}$) fluctuations, which causes the s-wave superconductivity without sign reversal ($s_{++}$-wave state). The derived orbital fluctuations also cause the instability toward the structure transition due to the bound state formation of two orbitons with opposite momenta, which is called the "two-orbiton process". Moreover, impurity-induced non-local orbital order with $C_2$-symmetry is obtained when the orbital fluctuations are strong. This "impurity-induced nematic state" explains the in-plane anisotropy of resistivity in detwinned samples. We stress that (i)-(iii) are reproducible only when orbital fluctuations with respect to $O_{xz}$ and $O_{yz}$ charge quadrupoles are the most divergent. This fact ensures the reliability of the present model Hamiltonian and calculation.