Fe₄Se₅ nanosheets were prepared by a chemical coprecipitation method. First, 200 ml of ethylene glycol was mixed with NaOH and SeO₂ powder and slowly heated up to 160°C for mixing well. The volume of 2.4 ml hydrazine hydrate was then added as the reducing agent. Then, at 160°C, the Fe precursor solution was added and reacted for 12 h in order to form Fe₄Se₅ nanosheets. The Fe precursor solution is made by dissolving the amount FeCl₂ in ethylene glycol. The reaction was done under N₂ gas purging to avoid the formation of oxide impurity. To clean the Fe₄Se₅ nanosheets, the reacted product was dispersed in acetone with absolute ethanol, and high-speed centrifugation is applied to precipitate the nanosheets and remove the capping ligand dissolved in the above organic solvent. The nanosheets were finally dried in a vacuum for 24 h and collected. The process for the rapid thermal annealing (RTA) is as follows: the as-grown Fe₄Se₅ nanosheets were heated at 450°C for 10 min in a tube furnace with 1 atm Ar gas inside to maintain a nonoxidation environment as a rapid thermal treatment process. After the rapid thermal treatment, an air-quenching process was taken by flowing room-temperature Ar gas through the tube. All the samples were stored in the oxygen-free glove box.

The crystal structure observation of the Fe₄Se₅ samples was carried out by the high-resolution transmission electron microscope (HRTEM, JEOL JEM-2100F) and 4-circle x-ray diffractometer with the incident beam (12.4 keV) of wavelength 0.82656 Å at beam-line BL13A and wavelength 0.61992 Å at beam-line TPS09A in NSRRC. The temperature-dependent structural information of Fe₄Se₅ samples was analyzed by the high-resolution neutron powder diffraction (high-resolution powder diffractometer Echidna with the wavelength of 2.4395 Å at ANSTO). The Fe₄Se₅ nanosheet powder was pressed into the pallet under 200 kg/cm² at 100°C for 1 h for the following measurements: To identify the stoichiometry, the energy-disperse X-ray spectrometer (EDS) setup with the SEM (JEOL JSM-7001F Field Emission Scanning Electron Microscope) was applied. To affirm the valence states of the Fe ions, the X-ray photoemission spectroscopy (XPS, VG Scientific ESCALAB 250) measurements for the samples were performed. For polycrystalline bulk samples, the resistance was measured by using the standard four-probe method with silver paste for electrical contact and the Hall measurement by a Hall-bar configuration was done by the Quantum Design Physical Properties Measurement System (PPMS, Model 6000). The magnetic property was measured by the Quantum Design Superconducting quantum interference device (SQUID, VSM).

Figure 1A shows the X-ray diffraction (XRD) patterns of the as-grown Fe₄Se₅ sample at room temperature. The diffraction pattern, which exhibits superstructure peaks, is refined with a tetragonal P4 symmetry with √5 × √5 Fe-vacancy order instead of the tetragonal P4/mmm symmetry as observed in FeSe [2]. The insets are the TEM image of as-grown Fe₄Se₅ nanocrystal and its TEM-SAED (selective area electron diffraction) patterns along the c-axis. The observation of extra diffraction points among the main diffraction points in the SAED pattern confirms the √5 × √5 Fe-vacancy order in the as-grown Fe₄Se₅ nanocrystal [35]. After RTA treatment at 450°C, the superstructure peaks observed in XRD and TEM-SAED due to the √5 × √5 Fe-vacancy order disappear, as shown in Figure 1B and its inset. The refinement results, using the same P4 symmetry, reveal that the occupations of Fe at vacancy 4d sites and the originally occupied 16i sites are almost the same, indicating that the Fe vacancies become disordered after RTA treatment. It is noted that the XRD patterns of the RTA treatment sample are nearly ten times smaller in the intensity response. This is due to the different synchrotron beamlines we used for our measurements. However, the difference does not affect the refined results.

It is noted that the FeSe₄ tetrahedron in as-grown Fe₄Se₅ is highly distorted due to the existence of the Fe-vacancy order. As the Fe vacancies disordered by the RTA treatment, the FeSe4 tetrahedron becomes more symmetric. The refined structure parameters are tabulated in Supplementary Tables S1 and S2. The EDS analysis confirms that the stoichiometries of samples keeps Fe₄Se₅ with Fe/Se ratio of 44.5 : 55.5 and 45.3 : 54.7 before and after the RTA treatment, respectively, as shown in Supplementary Figure S2 in the supplementary information.

Figure 2A shows the temperature dependence of the resistance for the as-grown polycrystalline pellet sample made of Fe₄Se₅ nanosheets. The inset is the magnetic susceptibility of the as-grown sample from 300 to 2 K. The R-T results of Fe₄Se₅ exhibit a metal-insulator transition with the sharp rise in resistance at ∼45 K. The data can be well-fitted to the three-dimensional Mott variable-range-hopping model (3D-MVH): ρ(Τ) = ρ ₀ exp(T ₀/Τ) ^ν , where T ₀ is the variable-range-hopping characteristic temperature, and the exponent υ is 1/(d+1) with d = 3 (the fitting results are shown in Supplementary Figure S2. A transition temperature T _V is marked as the onset temperature of 3D-MVH behavior). The variable-range-hopping characteristic temperature T ₀ calculated is ∼1,400 K for the as-grown sample. The magnetic susceptibility of the same sample shows paramagnetic behavior as the sample cools down from 300 K, and a sudden drop in susceptibility appears at about the same temperature as the resistance transition temperature (T _V) ∼45 K. The sharp resistive rise and the diamagnetic drop are the two signatures for the Verwey transition observed in Fe₃O₄, which occurs at 125 K. These results are also in line with those reported results in the Fe₄Se₅ nanowire, which was recently demonstrated to exhibit the Verwey-like electronic correlation [45].

Figure 2B shows the temperature-dependence resistance for the Fe₄Se₅ samples after 300° and 450 C RTA process. The sample after 300°C remains to behave like semiconductor. The sample treated at 450° and 300°C changes to metallic and becomes superconducting below ∼5 K with the onset superconductive critical temperature (T _c) ∼7.8 K, as evidenced in the upper-left inset of Figure 2B. The lower-right inset is the magnetic susceptibility, which further demonstrates the superconducting transition with onset T _c ∼ 7.9 K. The evolution to superconductivity in this RTA-treated sample is similar to that reported in the K_2-xFe_4+ySe₅ system, where superconductivity appears after Fe vacancies becoming disordered through high-temperature annealing and rapid quenching processes [43, 44].

In order to gain more insight into the observed Verwey-like electronic correlation, XPS at room temperature and temperature-dependent Hall measurements on the samples were performed. Figure 3A is the observed XPS results for the as-grown Fe₄Se₅ sample. Figure 3A is the observed XPS results for the as-grown Fe₄Se₅ sample. The XPS spectrum clearly reveals two peaks showing the existence of mixed-valence states of Fe. The observed two peaks, at 708.5 and 711.5 eV, can be associated with the Fe²⁺ and Fe³⁺ states, respectively. The best data fitting gives the ratio between Fe²⁺ and Fe³⁺ close to 1 : 1. This result is similar to that observed in the magnetite Fe₃O₄.

Figure 3B displays the XPS results for samples with RTA treated at 300° and 450°C. After the RTA treatment, the Fe³⁺ state becomes dominant. The extracted Fe³⁺ ion to total Fe atoms ratio is 58.7% for 300°C RTA-treated and 73.2% for 450°C RTA-treated samples, respectively, indicating a substantial increase in electron carriers in these samples. It should be noted that the sample after 300°C still exhibits temperature-dependent behavior like semiconductor. There is no specific difference of Se 3d peak at 54.7 eV before and after the RTA process of the Fe₄Se₅ sample according to the XPS result, as shown in Supplementary Figure S3.

It is known that tetragonal FeSe is a metal with two-band based on the first-principles electronic structure calculation, for example, by T. Xiang et al., [46]. T. Xiang et al. also reported that the electronic structure of Fe₄Se₅ with √5 × √5 Fe-vacancy order is a pair checkboard antiferromagnetic insulator. The calculation shows that the Fe-vacancy-ordered Fe₄Se₅ has a single-band structure with n-type carrier dominated and a bandgap ∼290 meV. Berlijn et al. [47] investigated the effect of disordered Fe vacancies on the normal-state electronic structure of the alkali-intercalated FeSe system, where the KFe₄Se₅ exhibits exactly the same Fe-vacancy order as that in Fe₄Se₅. They found that the disorder of Fe-vacancy can effectively raise the chemical potential giving enlarged electron pockets without adding carriers to the system.

It is noted that, as reported by Chen et al. [38], there exists a series of Fe_xSe_y compounds with x/y = 1/2, 2/3, 3/4, 4/5, etc. We have carried out a systematic study using the coprecipitation method to successfully prepare tetragonal Fe_(1-x)Se with stoichiometry of Fe₃Se₄ and Fe₄Se₅. Based on the XPS results, the observed Fe³⁺/Fe²⁺ ratio is 2 and 1 for tetragonal Fe₃Se₄ and Fe₄Se₅, respectively, as shown in Supplementary Figure S4A and Figure 3A. These data imply that Fe₃Se₄ would be hole-doped and Fe₄Se₅ be electron-doped if there are additional carriers based on the simple charge balance picture by considering Fe₃Se₄ to be the combination of Fe⁽²⁺⁾Se and Fe₂ ⁽³⁺⁾Se₃, whereas Fe₄Se₅ is from 2(Fe⁽²⁺⁾Se) and Fe₂ ⁽³⁺⁾Se₃. Indeed, our Hall measurement results show at 300 K a hole concentration of 1.20 × 10¹⁹/cm³ for Fe₃Se₄ (Supplementary Figure S4B) and electron concentration of −6.52 × 10¹⁷/cm³ for Fe₄Se₅.

Both of the as-grown and RTA-treated Fe₄Se₅ show a single-band behavior with n-type carrier from the Hall resistivity measurements, as shown in Supplementary Figure S5. The Hall coefficient of the as-grown sample at room temperature is −9.59 cm³/C, corresponding to the electron carrier concentration of 6.52 × 10¹⁷ cm⁻³, and the carrier concentration decreases by about a factor of 8 at the transition temperature T _V, as shown in Figure 3C.

After the Fe₄Se₅ sample is RTA-treated at 450 °C, the Fe³⁺/Fe²⁺ ratio becomes close to 3 : 1, which means that a large number of electrons are introduced and subsequently induced superconductivity. Indeed, the Hall measurement results, as shown in Figure 3D, show that the carrier concentration at 300 K increases to −3.34 × 10²¹/cm³ (Hall coefficient −1.87 × 10⁻³ cm³/C) for 450 C RTA-treated sample. The electron carrier concentration is about four orders of magnitude increase comparing with the as-grown Fe₄Se₅. Obviously, the RTA treatment disrupts the Fe-vacancy long-range order and leads to the increase of electron carriers.

It is well known that the Verwey transition in magnetite exhibits a structural transition accompanied by the sharp resistive and magnetic susceptibility changes. To examine whether such a structural change exists for the as-grown Fe₄Se₅, we have carried out the neutron diffraction at low temperatures.

The detailed structural information of the as-grown Fe₄Se₅ sample measured by neutron diffraction at different temperatures is shown in Figure 4. At room temperature, the neutron data, consistent with XRD results, fit well with the P4-tetragonal symmetry. At low temperatures, a distortion appears at temperatures below 30 K. The data at 5 K, with evident peak emergence shown in the inset of Figure 4, indicates a possible structural change. This result further supports that the as-grown Fe₄Se₅ nanosheets, similar to the results observed in Fe₄Se₅ nanowire, show the Verwey-like correlation. The Verwey-like transition temperature of ∼45 K in nanosheets is higher than that observed in the nanowire, which was found to be ∼30 K. This shows the size dependence of T _V, which is also noticed in Verwey transition [48–50]. Currently, we are waiting for the results of the detailed high-resolution XRD at low temperatures using a synchrotron source to determine exactly the low-temperature phase and the transition temperature.