Model of the Electronic Structure of Electron-Doped Iron-Based Superconductors: Evidence for Enhanced Spin Fluctuations by Diagonal Electron Hopping

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 between 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.

Figure 1

Fermi surfaces for $x=0.05$, $x=0.15$, $x=0.25$, $x=0.35$ with (a) $\mathrm{\Delta }\alpha =-1°$ or (b) $\mathrm{\Delta }\alpha =+1°$.

Figure 2

Eigenvalue of the Eliashberg equation against doping. (a) $\lambda$ against doping for $\mathrm{\Delta }\alpha =-1$, 0, $+1$, $+2°$. (b) Similar as in (a) for $\mathrm{\Delta }\alpha =-3$, $-2$, $-1°$. (c) $\lambda$ for simplified models in which only $t_1$ is varied in conjunction with $x$ so as to maintain the volume of the ($\pi$, $\pi$) Fermi surface. The numbers are the values of $t_1$ (in eV). Here, $t_2$ is fixed at 0.106 (0.113) eV for $\mathrm{\Delta }\alpha =-1(+1)$. See text for more details. Upper right panel: Experimental result of $T_c$ vs $x$ for LnFeAs(O,H) with $\mathrm{Ln}=\mathrm{Gd}$, Sm, Ce, and La (from Ref. [14]).

Figure 3

Intraorbital spin susceptibilities ${\chi }_{xy}$ and ${\chi }_{xz/yz}$ for $x=0.05$, 0.15, and 0.25. (a) $\mathrm{\Delta }\alpha =-1°$ and (b) $\mathrm{\Delta }\alpha =+1°$.

Figure 4

Upper panels: doping dependence of the real space hopping integrals $t_1$ and $t_2$ against the doping. (a) $\mathrm{\Delta }\alpha =+1°$ (red or gray) and $\mathrm{\Delta }\alpha =-1°$ (black). Solid (dashed) lines are $t_2$ ($t_1$). (b) Actual materials La1111(red or gray) and Sm1111(black). Circles (boxes) are $t_1$ ($t_2$). Lower panels: schematic figure of the origin of the prioritized diagonal hopping with doping.

Figure 5

Schematic figure of the spin fluctuation contribution to superconductivity.