Doping-induced antiferromagnetic bicollinear insulating state and superconducting temperature of monolayer FeSe systems

First-principles calculations of ionic-liquid-gated (Li,Fe)OHFeSe suggest a metal-insulator transition at a nominal Li/Fe ratio of 75/25 in the (Li,Fe)OH layer. While doping increases Fermi energy, the formation of an antiferromagnetic bicollinear phase is the key for the transition. It is expected that this insulating phase also exists in other FeSe systems upon heavy electron doping, and its presence can hinder the increase of superconducting temperature. These results offer clues on how to optimize superconductivity amid its interplay with magnetic properties in FeSe systems.

Figure 1

(a) Side and (b) top views of the supercell used in the calculation of (Li,Fe)OHFeSe, where brown, green, dark green, red, and pink balls are the Fe, Se, Li, O, and H atoms, respectively.

Figure 2

Spin texture of the (a) CO, (b) BI, and (c) PA phases. (d) Cross section of the total charge density $\rho$ in the Fe plane for the BI phase. Fe double dimers are clearly visible in the plot.

Figure 3

Bottom: A schematic illustration of the effects due to applied gate voltage. (Li,Fe)OHFeSe is known to contain Li vacancies in the spacer. Increasing gate voltage first fills up the vacancies by Li ions, but then it replaces irons on the Li sites. Top: Energy diagram of magnetically ordered CO, BI, PA, and NE phases. The dashed line with open circles is for the BI phase without atomic relaxation. Vertical lines indicate the phase boundaries. Number pairs in the parentheses denote (${\mathrm{Fe}}_{\mathrm{Li}}$/${\mathrm{V}}_{\mathrm{Li}}$) in the supercell. The corresponding [Li] in the spacer is given near the bottom. The number of electrons donated by the spacer to the FeSe layer is also indicated (using the scale to the right).

Figure 4

Band structures of (a)–(c) CO and (d)–(f) BI phases. (a) and (d) Undoped ML FeSe, and (b) and (e) (0.25 electrons per Fe)-doped ML FeSe, and (c) and (f) ${\mathrm{Li}}_{0.75}{\mathrm{Fe}}_{0.25}\mathrm{OHFeSe}$ [with $\left(\mathrm{F}{\mathrm{e}}_{\mathrm{Li}}/{\mathrm{V}}_{\mathrm{Li}}\right)=\left(4/0\right)]$. Horizontal dotted lines denote $E_F$ positions. While bands for the same chemical system are naturally aligned, between different systems, they are aligned according to deep Se $s$ bands. Each state in (c) and (f) is projected onto the FeSe layer. The larger the projection, the darker the dot used for that state.

Figure 5

The energy difference between CO and BI phases with respect to the $U$ value used in the PBE+U calculation for (a) (Li,Fe)OHFeSe $\left(\mathrm{F}{\mathrm{e}}_{\mathrm{Li}}/{\mathrm{V}}_{\mathrm{Li}}\right)=\left(4/2\right)$ and (b) 0.25-electron doped FeSe. For $U>0.5$ eV, the BI phase becomes stable in both systems.