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.
We theoretically study the spin fluctuation and superconductivity in La1111 and Sm1111 iron-based superconductors for a wide range of electron doping. When we take into account the band structure variation by electron doping, the hole Fermi surface o
riginating from the $d_{X^2-Y^2}$ orbital turns out to be robust against electron doping, and this gives rise to large spin fluctuations and consequently $spm$ pairing even in the heavily doped regime. The stable hole Fermi surface is larger for Sm1111 than for La1111, which can be considered as the origin of the apparent difference in the phase diagram.
We perform first principles band calculation of the newly discovered superconductor LaO$_{1-x}$F$_x$BiS$_2$, and study the lattice structure and the fluorine doping dependence of the gap between the valence and conduction bands. We find that the dist
ance between La and S as well as the fluorine doping significantly affects the band gap. On the other hand, the four orbital model of the BiS$_2$ layer shows that the lattice structure does not affect this portion of the band. Still, the band gap can affect the carrier concentration in the case of light electron doping, which in turn should affect the transport properties.
High-temperature cuprate superconductors have been known to exhibit significant pressure effects. In order to fathom the origin of why and how Tc is affected by pressure, we have recently studied the pressure effects on Tc adoptig a model that contai
ns two cupper d-orbitals derived from first-principles band calculations, where the dz2 orbital is considere on top of the usually considered dx2-y2 orbital. In that paper, we have identified two origins for the Tc enhancement under hydrostatic pressure: (i) while at ambient pressure the smaller the hybridization of other orbital components the higher the Tc, an application of pressure acts to reduce the multiorbital mxing on the Fermi surface, which we call the orbital distillation effects, and (ii) the increase of the band width with pressure also contributes to the enhancement. In the present paper, we further elabolrate the two points. As for point (i), while the reduction of the apical oxygen height under pressure tends to increase the dz2 mixture, hence to lower Tc, here we show that this effect is strongly reduced in bi-layer materials due to the pyramidal coordination of oxygen atoms. As for point (ii), we show that the enhancement of Tc due to the increase in the band width is caused by the effect that the many-body renormalization arising from the self-energy is reduced.
The origin of uniaxial and hydrostatic pressure effects on $T_c$ in the single-layered cuprate superconductors is theoretically explored. A two-orbital model, derived from first principles and analyzed with the fluctuation exchange approximation give
s axial-dependent pressure coefficients, $partial T_c/partial P_a>0$, $partial T_c/partial P_c<0$, with a hydrostatic response $partial T_c/partial P>0$ for both La214 and Hg1201 cuprates, in qualitative agreement with experiments. Physically, this is shown to come from a unified picture in which higher $T_c$ is achieved with an orbital distillation, namely, the less the $d_{x^2-y^2}$ main band is hybridized with the $d_{z^2}$ and $4s$ orbitals higher the $T_c$. Some implications for obtaining higher $T_c$ materials are discussed.
We study the relation between the spin fluctuation and superconductivity in an heavily hole doped end material KFe$_2$As$_2$. We construct a five orbital model by approximately unfolding the Brillouin zone of the three dimensional ten orbital model o
btained from first principles calculation. By applying the random phase approximation, we obtain the spin susceptibility and solve the linearized Eliashberg equation. The incommensurate spin fluctuation observed experimentally is understood as originating from interband interactions, where the multiorbital nature of the band structure results in an electron-hole asymmetry of the incommensurability in the whole iron-based superconductor family. As for superconductivity, s-wave and d-wave pairings are found to be in close competition, where the sign change in the gap function in the former is driven by the incommensurate spin fluctuations. We raise several possible explanations for the nodes in the superconducting gap of KFe$_2$As$_2$ observed experimentally.
We examine theoretically the superconducting state of BaFe$_2$(As$_{1-x}$P$_x$)$_2$, an isovalent doping 122 iron pnictide superconductor. We construct a three dimensional ten orbital model from first principles band calculation, and investigate the
superconducting gap within the spin fluctuation mediated pairing mechanism. The gap is basically $spm$, where the gap changes its sign between electron and hole Fermi surfaces, but three dimensional nodal structures appear in the largely warped hole Fermi surface having strong $Z^2/XZ/YZ$ orbital character. The present result, together with our previous study on 1111 systems, explains the strong material dependence of the superconducting gap in the iron pnictides.
In order to explore the reason why the single-layered cuprates, La$_{2-x}$(Sr/Ba)$_x$CuO$_4$ ($T_csimeq$ 40K) and HgBa$_2$CuO$_{4+delta}$ ($T_csimeq$ 90K), have such a significant difference in $T_c$, we study a two-orbital model that incorporates th
e $d_{z^2}$ orbital on top of the $d_{x^2-y^2}$ orbital. It is found, with the fluctuation exchange approximation, that the $d_{z^2}$ orbital contribution to the Fermi surface, which is stronger in the La system, works against d-wave superconductivity, thereby dominating over the effect of the Fermi surface shape. The result resolves the long-standing contradiction between the theoretical results on Hubbard-type models and the experimental material dependence of $T_c$ in the cuprates.
We study the effect of the lattice structure on the spin-fluctuation mediated superconductivity in the iron pnictides adopting the five-band models of several virtual lattice structures of LaFeAsO as well as actual materials such as NdFeAsO and LaFeP
O obtained from the maximally-localized Wannier orbitals. Random phase approximation is applied to the models to solve the Eliashberg equation. This reveals that the gap function and the strength of the superconducting instability are determined by the cooperation or competition among multiple spin fluctuation modes arising from several nestings among disconnected pieces of the Fermi surface, which is affected by the lattice structure. Specifically, the appearance of the Fermi surface $gamma$ around $(pi,pi)$ in the unfolded Brillouin zone is sensitive to the pnictogen height $h_{rm Pn}$ measured from the Fe plane, where $h_{rm Pn}$ is shown to act as a switch between high-$T_c$ nodeless and low-$T_c$ nodal pairings. We also find that reduction of the lattice constants generally suppresses superconductivity. We can then combine these to obtain a generic superconducting phase diagram against the pnictogen height and lattice constant. This suggests that NdFeAsO is expected to exhibit a fully-gapped, sign-reversing s-wave superconductivity with a higher $T_c$ than in LaFeAsO, while a nodal pairing with a low $T_c$ is expected for LaFePO, which is consistent with experiments.
