Phase Diagram and a Possible Unified Description of Intercalated Iron Selenide Superconductors

We propose a theoretical description of the phase diagram and physical properties in $A_2{\mathrm{Fe}}_4{\mathrm{Se}}_5$-type ($A=K$, Tl) compounds based on a coexistent local moment and itinerant electron picture. Using neutron scattering and angle-resolved photoemission spectroscopy measurements to fix the general structure of the local moment and itinerant Fermi pockets, we find a superconducting phase with $s$-wave pairing at the $M$ pockets and an incipient sign-change $s$ wave near the $\Gamma$ point, which is adjacent to the insulating phases. The uniform susceptibility and resistivity are found to be consistent with the experiment. The main distinction with iron pnictide superconductors is also discussed.

Figure 1

(a) Top view of the Fe (denoted by circles) layer with $1/5$ Fe vacancies ordered in the right-handed rotation. The block AF ordering is indicated by the opposite arrows. The shaded square is the 1-Fe unit cell used throughout this work. The dashed square is the enlarged $\sqrt{5}\times \sqrt{5}$ unit cell for the vacancy ordering. (b) Bare band structure of the itinerant electrons. (c) $\Gamma$, $M_1$, and $M_2$ points in the 1-Fe BZ. Black circles around $M$ points indicate the Fermi surface at $\mu =50\mathrm{meV}$. Shaded square regions are the folded BZ’s for the right-handed lattice, while the dashed circles of a radius $K$ mark the averaged BZ’s (see text). The AF wave vectors, ${\mathbf{Q}}_{s1}$ and ${\mathbf{Q}}_{s2}$, are defined in the text. (d) The density of states with the band gap induced by the Fe vacancy order.

Figure 2

The pairing symmetry and strength characterized by $f_A(\mathit{k}){\Delta }_A(\mathit{k})$: (a) The electron doped case at $\mu =+50\mathrm{meV}$ (relevant to reality); (b) The undoped case at $\mu =0\mathrm{meV}$; (c) The hole doped case at $\mu =-50\mathrm{meV}$.

Figure 3

The global phase diagram at different interpocket gaps: (a) ${ϵ}_0=10\mathrm{meV}$; (b) ${ϵ}_0=15\mathrm{meV}$. Notations, $\Gamma$-SC and $M$-SC, stand for the SC on $\Gamma$ pockets and $M$ pockets, respectively. The resistivity is calculated outside the SC phases, with darker background indicating higher resistivity.

Figure 4

(a) The uniform magnetic susceptibility ${\chi }_u={\chi }_{\mathrm{it}}+{\chi }_{\mathrm{loc}}$ at $\mu =50\mathrm{meV}$. The (red) dotted curve: itinerant electron part ${\chi }_{\mathrm{it}}$; The (blue) dashed curve: local moment part ${\chi }_{\mathrm{loc}}$. (b) dc resistivity calculated at different $\mu$’s, corresponding to different electron dopings in Fig. 3b, including two insulating regimes and the AF metal regime in between, with the SC transition at low temperatures.