Orbital-Selective Superconductivity and the Effect of Lattice Distortion in Iron-Based Superconductors

The superconducting (SC) state of iron-based compounds in both tetragonal and orthorhombic phases is studied on the basis of an effective Hamiltonian composed of the kinetic energy including the five Fe 3d-orbitals, the orthorhombic crystalline electric field (CEF) energy, and the two-orbital Kugel'-Khomski\u{i}-type superexchange interaction. Our basic assumption is that the antiferromagnetic (AF) state in the parent compounds can be described by the $d_{xz}$ and $d_{yz}$ orbitals, and that the electrons in these orbitals have relatively strong electron correlation in the vicinity of the AF state. In order to study the physical origin of the structure-sensitive SC transition temperature, the effect of orthorhombic distortion is taken into account as the energy-splitting, $\Delta_{\textrm{ortho.}}$, between the $d_{xz}$ and $d_{yz}$ orbitals. We find that the eigenvalue of the linearized gap equation decreases accompanied with the reduction of the partial density of states for the $d_{xz}$ and $d_{yz}$ orbitals as $\Delta_{\textrm{ortho.}}$ increases, and that the dominant pairing symmetry is an unconventional fully gapped $s_{+-}$-wave pairing. We also find large anisotropy of the SC gap function in the orthorhombic phase. We propose that the CEF energy plays an important role in controlling $T_{\textrm{c}}$ and the SC gap function, and that orbital-selective superconductivity is a key feature in iron-based superconductors, which causes the structure-sensitive $T_{\textrm{c}}$.