High-temperature (high-$T_{rm c}$) superconductivity appears as a consequence of the carrier-doping of an undoped parent compound exhibiting antiferromagnetic order; thereby, ground-state properties of the parent compound are closely relevant to the
superconducting state. On the basis of the concept, a spin-fluctuation has been addressed as an origin of pairing of the superconducting electrons in cuprates. Whereas, there is growing interest in the pairing mechanism such as an unconventional spin-fluctuation or an advanced orbital-fluctuation due to the characteristic multi-orbital system in iron-pnictides. Here, we report the discovery of an antiferromagnetic order as well as a unique structural transition in electron-overdoped LaFeAsO$_{1-x}$H$_x$ ($x$ ~ 0.5), whereby another parent phase was uncovered, albeit heavily doped. The unprecedented two-dome superconducting phases observed in this material can be interpreted as a consequence of the carrier-doping starting from the original at $xsim0$ and advanced at $xsim0.5$ parent phases toward the intermediate region. The bipartite parent phases with distinct physical properties in the second magnetic phase provide us with an interesting example to illustrate the intimate interplay among the magnetic interaction, structural change and orbital degree of freedom in iron-pnictides.
We present a theoretical understanding of the superconducting phase diagram of the electron-doped iron pnictides. We show that, besides the Fermi surface nesting, a peculiar motion of electrons, where the next nearest neighbor (diagonal) hoppings bet
ween iron sites dominate over the nearest neighbor ones, plays an important role in the enhancement of the spin fluctuation and thus superconductivity. In the highest $T_c$ materials, the crossover between the Fermi surface nesting and this prioritized diagonal motion regime occurs smoothly with doping, while in relatively low $T_c$ materials, the two regimes are separated and therefore results in a double dome $T_c$ phase diagram.
Iron arsenide superconductors based on the material LaFeAsO1-xFx are characterized by a two-dimensional Fermi surface (FS) consisting of hole and electron pockets yielding structural and antiferromagnetic transitions at x = 0. Electron doping by subs
tituting O2- with F- suppresses these transitions and gives rise to superconductivity with a maximum Tc = 26 K at x = 0.1. However, the over-doped region cannot be accessed due to the poor solubility of F- above x = 0.2. Here we overcome this problem by doping LaFeAsO with hydrogen. We report the phase diagram of LaFeAsO1-xHx (x < 0.53) and, in addition to the conventional superconducting dome seen in LaFeAsO1-xFx, we find a second dome in the range 0.21 < x < 0.53, with a maximum Tc of 36 K at x = 0.3. Density functional theory calculations reveal that the three Fe 3d bands (xy, yz, zx) become degenerate at x = 0.36, whereas the FS nesting is weakened monotonically with x. These results imply that the band degeneracy has an important role to induce high Tc.
