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

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... timize superconductivity amid its interplay with magnetic properties in FeSe systems. * Corresponding authors: jbang0312@kbsi.re.kr and zhangs9@rpi.edu The discovery of iron oxy-pnictide superconductor LaOFeP with a superconducting transition temperature = 4 K [1] has laid the foundation for iron-based superconductivity. Not only are the materials non-ceramics, but also it contains ferromagnetic elements, i.e., iron, in spite of the incompatibleness between superconductivity and magnetism, which makes the ironbased materials exceptionally interesting. Within the iron-superconductor family, layered FeSe, with = 8.5 K [2] in ambient pressure, has emerged as a subject of intense study, as a as high as > 100 K [3] (which is more than tenfold of the bulk value) may be obtained by placing a monolayer (ML) FeSe on a SrTiO 3 (STO) substrate. This result is truly exceptional, as many experiments have shown that, even at the optimal condition, of a FeSe-derived superconductors is in the neighborhood of or below 40 K, for examples, the highest = 32 K for K x Fe 2-y Se 2 [4], 31 K for (Tl,K)Fe x Se 2 [5], and 36.7 K for FeSe under pressure [6]. It hints for a unique mechanism of the superconductivity in the ML FeSe system. For example, recent experimental and theoretical studies showed that interfacial electron-phonon coupling may play a role for the significantly enhanced [7-10]. As having been shown in cuprates and other Fe-based superconductors, the interplay between magnetism and superconductivity, as reflected in their phase diagrams, are sensitive to carrier doping and applied pressure. As such, the phase diagram holds the key to the understanding of the superconductivity. An interrogation of such an interplay in the FeSe systems is, however, hindered by the low stability and phase separation [11,12]. Recently, a new FeSe superconductor, (Li,Fe)OHFeSe, which can be viewed as a stack of ML FeSe separated by (Li,Fe)OH spacers [11-18], has emerged, which is suitable for the study of phase diagram by gate-tunable ionic liquid doping [12]. By this approach, up to 43 K, which is similar to the highest for other FeSe-derived superconductors, is observed. Unfortunately, however, a further increase of by doping is hindered by the formation of an unknown antiferromagnetic (AFM) insulating phase. Alternatively, the AFM phase in (Li,Fe)OHFeSe may be related to the insulating phase of heavily-doped FeSe, which is a result of an electronic correlation effect [19]. In the heavilydoped ML FeSe on STO, on the other hand, increases monotonically without such an insulating phase [20], whereby defying all the odds. One may, therefore, wonder if a further increase of is indeed possible without invoking any unconventional superconductivity theory, when the formation of the AFM insulating phase can be suppressed. In this paper, first-principles density functional theory (DFT) is used to study the mysterious AFM insulating phase, which is identified as the bicollinear (double-stripe) (BI) phase in (Li,Fe)OHFeSe. It becomes stable at a Li/Fe ratio of 75/25 in the (Li,Fe)OH layer, i.e., 0.25 electron/Fe doping at the FeSe layer, and is stabilized by an spin-phonon coupling to result in a large iron relaxation of 7% and Fe double-dimers. A phase diagram for (Li,Fe)OHFeSe is thus established: at low gate voltage, a ground-state AFM metallic collinear (CO) phase has the lowest energy, and the superconductivity can arise in close proximity to this AFM CO phase. As the gate voltage increases, the BI phase becomes stable. When the gate voltage increases further, the system transitions back to the CO phase, and finally to an insulating pair-checkerboard (PA) phase. The transition to BI phase by gate voltage is in qualitative agreement with available experiments [12]. The BI phase is expected to be stable in other heavily-doped FeSe systems, as well. Hence, one must avoid the BI phase in order to further increase , as may be the case in ML FeSe on STO. The calculations employ the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional [21], which describes reasonably well the (Li,Fe)OHFeSe system [15]. Iron-based superconductors are typically moderately correlated materials, and correlation effects beyond PBE can thus be important. Hence, we have used the PBE + approach [22] with 0.5 eV (taken from the literature [23]) for Fe 3d electrons. We have also considered larger values up to 4.3 eV [24], but the qualitative results do not depend on the used in the calculation (See below). The projected augmented wave potential method [25] is employed for Fe (4s, 3d) and Se (4s, 4p) electrons, as implemented in the VASP code [26]. Van der Waals interactions are included via the DFT + D2 method [27]. The wave functions are expanded in a plane wave basis up to a cutoff energy of 400 eV. The Brillouin zone of the supercell (see below) is sampled by a Monkhorst-Pack 4×4×5 k-point mesh. The electronic structure calculations are converged to 10 -6 eV, whereas the atomic structures are relaxed until the forces are less than 0.01 eV/Å. We use an 80-atom supercell with 16 formula units of LiOHFeSe. Figure 1 shows, as an example, (a) a perspective side view and (b) a top view of the Li 0.75 Fe 0.25 OHFeSe supercell where there are Fe atoms substituting Li atoms in the LiOH spacer ( ), but no Li vacancy ( ). In this study, up to six defects [i.e., 4 + 2 , or ( / ) = (4/2)] are considered. In principle, different occupations of the lattice sites by the defects can affect the calculated results. corresponding CO phases by 20 and 4 meV/1x1, respectively. In 0.25-doped bulk FeSe, on the other hand, the BI phase is higher in energy than the CO phase by 22 meV/1x1; an even higher doping level of 0.5 electron per Fe is thus required to stabilize it. This explains why in bulk FeSe insulating phase only exists in high-doping regime over the superconducting dome [19], but in Li 0.75 Fe 0.25 OHFeSe it appears below or at the optimal doping level [12]. For ML FeSe on STO, however, experimental evidence of the BI phase is not yet available. As discussed in Ref. [44], the ML FeSe strongly binds to STO substrate. As such, the formation of Fe-Fe-Fe double dimers may be prohibited, which prevents the formation of insulating BI phase. From the above, we may better understand the superconducting physics of (Li,Fe)OHFeSe. First, there should be a limit on the increase of due to the formation of the insulating BI phase. It is noted that spin fluctuation near the transition to the BI phase may enhance the superconductivity, provided that the free-carrier concentration remains high. The formation of the insulating BI phase, however, eliminates the free carriers, whereby putting an upper bound to the increase of . Indeed, in experiments [12], increases with electron doping but transitions into an insulating phase at = 43K. Second, our results suggest that one should avoid replacing substitutional iron, , by , as this would decrease, rather than increasing, electron doping. Also, replacing by is kinetically much harder than filling up Li vacancies, .