Emergence of superconductivity in (NH3)yMxMoSe2 (M: Li, Na and K)

We report syntheses of new superconducting metal-doped MoSe2 materials (MxMoSe2). The superconducting MxMoSe2 samples were prepared using a liquid NH3 technique, and can be represented as ‘(NH3)yMxMoSe2’. The Tcs of these materials were approximately 5.0 K, independent of x and the specific metal atom. X-ray diffraction patterns of (NH3)yNaxMoSe2 were recorded using polycrystalline powders. An increase in lattice constant c showed that the Na atom was intercalated between MoSe2 layers. The x-independence of c was observed in (NH3)yNaxMoSe2, indicating the formation of a stoichiometric compound in the entire x range, which is consistent with the x-independence of Tc. A metallic edge of the Fermi level was observed in the photoemission spectrum at 30 K, demonstrating its metallic character in the normal state. Doping of MoSe2 with Li and K also yielded superconductivity. Thus, MoSe2 is a promising material for designing new superconductors, as are other transition metal dichalcogenides.

Searching for new superconducting materials is one of the most challenging and exciting areas of research. During the past decade, iron pnictides (FeAs) and chalcogenides (FeSe) have attracted much attention, not only from researchers interested in developing new superconductors, but also physicists who are interested in the mechanism of superconductivity [1][2][3][4] . Recently, syntheses of metal-intercalated systems of FeSe using a liquid NH 3 technique have been extensively studied because various superconductors with high superconducting transition temperatures (T c s) have been discovered [5][6][7][8] ; the highest T c s are 46 K at ambient pressure 5 and 49 K at high pressure 9 . The pressure-induced enhancement of T c has also been confirmed for non-NH 3 K x FeSe 10 . Thus a layered compound like FeSe is a promising material platform for investigating high-T c superconductors.
The Mo dichalcogenide family has also attracted much attention because of the emergence of its unique physical properties 11,12 and potential use in high-speed transistors 13,14 . Electrostatic electron-doping of MoS 2 has produced superconductivity with a T c as high as 10.8 K 11 . The plot of T c versus the accumulated two-dimensional (2D) electron density n 2D showed a dome-shaped curve, i.e., the T c was tuned by the extent of electrostatic electron-doping. The maximum T c was 10.8 K at 1.2 × 10 14 cm −2 . Also, a signature of 2D superconductivity was observed in electrostatically electron-accumulated MoS 2 11 . The chemical doping of MoS 2 with alkali and alkaline-earth metal atoms 15,16 provided superconductivity with T c s lower than the maximum T c of electrostatically electron-accumulated MoS 2 11,12 . The chemical doping of MoS 2 was achieved using the liquid NH 3 technique, and many superconducting materials have been produced.
Very recently, electron-doping of MoSe 2 was achieved by the electrostatic method 17 , and the T c was precisely tuned in the same manner as in MoS 2 . In the case of MoSe 2 , only a Sr atom was intercalated, and MoSe 2 then showed a T c as high as 5.0 K 15 . This sample was prepared using the liquid NH 3 technique, and the chemical composition of Sr x MoSe 2 can be expressed as '(NH 3 ) y Sr x MoSe 2 ' , where the nominal x was 0.2. The shielding fraction of (NH 3 ) y Sr 0.2 MoSe 2 was 60%.
Here, we report syntheses of M x MoSe 2 samples (M: Li, K and Na) using the liquid NH 3 technique. In this study, Li, Na, K and Sr atoms were intercalated into MoSe 2 solids (only Sr-intercalation had previously been reported) 15 .

Results
Crystal structure of (NH 3 ) y Na x MoSe 2 . Single crystals of pristine MoSe 2 were prepared using the annealing technique; details are described in the Methods section. A photograph of a pure MoSe 2 sample is shown in Figure S1a. A single-crystal structure analysis was produced using a piece of MoSe 2 (or single crystal) separated from a MoSe 2 agglomeration prepared in this study ( Figure S1a); it is unclear whether an entire agglomeration is a single crystal or consists of multiple single crystals. A reasonable residual-factor (R) could be obtained in this analysis (R = 2.4% and weighted R (wR) = 4.6%). Only one phase of MoSe 2 was included in the single crystal, and it was confirmed that no other phase such as Mo 3 Se 4 was included. The structure of the MoSe 2 single crystal was hexagonal (space group: No. 194, P6 3 /mmc). The lattice constants were a = 3.289(7) Å and c = 12.96(3) Å, which are consistent with those (a = 3.283 Å and c = 12.918 Å) reported previously for pristine MoSe 2 18 . Crystallographic data are listed in Table S1. As seen from the magnetic susceptibility M/H (emu g −1 = cm 3 g −1 ) shown in Figure S2, no superconductivity was observed in any precursor MoSe 2 sample, implying no contamination with superconducting Mo 3 Se 4 . The chemical composition of one MoSe 2 agglomeration was determined to be 'MoSe 1.9(2) ' from the EDX spectrum ( Figure S3). These analyses also show that the precursor material was not superconducting Mo 3 Se 4 19 , i.e., it was non-superconducting MoSe 2 . The EDX spectra, magnetic susceptibilities and single-crystal analyses guaranteed that all MoSe 2 agglomerations used for metal-intercalation throughout this study were in fact substantially 'MoSe 2 ' .
Metal-doped MoSe 2 samples were prepared using the liquid NH 3 technique. The experimental details are described in the Methods section. Here, it is worth noting that instead of a polycrystalline powder, in this study, an agglomeration of MoSe 2 was used as the starting material for metal-intercalation. This is based on the successful synthesis of metal-doped FeSe from an agglomeration of FeSe 20 .
A photograph of (NH 3 ) y Na 0.5 MoSe 2 prepared using the liquid NH 3 method is shown in Fig. 1a; the stoichiometry of Na (x = 0.5) is an experimental nominal value. The (NH 3 ) y Na 0.5 MoSe 2 samples (agglomerations) look like single crystals. The EDX spectrum for (NH 3 ) y Na 0.5 MoSe 2 is shown in Figure S4, which shows that the (NH 3 ) y Na 0.5 MoSe 2 sample is (NH 3 ) 0.4(1) Na 0.41(1) MoSe 2.04 (1) . The amount of NH 3 , y = 0.4(1), was determined from the mass difference before and after the reaction that used liquid NH 3 . These results indicate that NH 3 was included in this material, and the amount of Na is reasonably consistent with the experimental nominal value. Here, we must consider the exact chemical structure and appropriate representation of NH 3 , i.e., which form exists in the MoSe 2 solid? Does it exist as molecular NH 3 , or does it take some other form such as a metal-coordinated amide? To determine the exact chemical formula, neutron diffraction may be required. Throughout this paper the simple chemical formula, (NH 3 ) y M x MoSe 2 , is used for convenience because the exact chemical form of NH 3 is unclear.
The structure of (NH 3 ) y Na 0.5 MoSe 2 (0.5 is a nominal experimental value) was examined as a typical example using single-crystal XRD data collected at room temperature. As seen in Figure S1b, the XRD Bragg spots are quite diffuse, indicating a very disordered crystal. Because of the diffuse spots, a definitive structural analysis could not be performed.
To confirm whether the Na atom is located midway in the space between MoSe 2 layers, the powder XRD pattern of (NH 3 ) y Na 0.5 MoSe 2 was measured with synchrotron radiation (λ = 0.4137(1) Å). The XRD pattern is shown in Fig. 1b together with the pattern calculated based on Le Bail fitting. The Le Bail fitting was performed for two phases under the space group of P6 3 /mmc. The sample was prepared from Na and MoSe 2 using the liquid NH 3 technique, and ground up for the acquisition of a powder XRD pattern. The a and c of the main phase were determined to be 3.541(2) and 14.810(4) Å, respectively, while those of the minor phase were 3.2615(1) and 12.8133(5) Å. The minor phase can be assigned to pure MoSe 2 , the lattice constants of which are consistent with the values (a = 3.289(7) Å and c = 12.96(3) Å) determined for pure MoSe 2 single crystal in this study. As seen from Fig. 1b, the peak-intensity of 002 peaks for non-doped (minor) and Na-doped MoSe 2 (major) observed at angles below 2θ = 5° were virtually the same, indicating that the fractions were almost equivalent. No other phase (such as metal-doped Mo 3 Se 4 ) was found, which is reasonable because the precursor material before metal-doping was demonstrated to be MoSe 2 .
The c of 14.810 Å of the main phase is larger by 1.85 Å than that of pure MoSe 2 (12.96(3) Å), indicating that the Na is located in the space between MoSe 2 layers. The a value also increased to 3.541(2) Å from 3.289(7) Å, but the expansion (Δ a = 0.252 Å) is too small to be attributed to the intercalation of Na into the MoSe 2 layer. As discussed later, the intercalation of Na at a 2a site, i.e., the space between MoSe 2 layers, seems to be the most reasonable explanation of the observed changes. The R and weighted pattern R (wR p ) were 3.2 and 4.8% in the Le Bail fitting, respectively, which are reasonable values that confirm the Le Bail analysis. The structure suggested is shown in Fig. 1c; in this structure, NH 3 is not shown. A more precise crystal structure that includes NH 3 must be determined using high-quality (NH 3 ) y Na 0.5 MoSe 2 single crystals that yield sharp Bragg spots. This study is now in progress.
In this study, we tried to perform Rietveld refinement based on the model listed in Table S2 of Supplementary Information; the atomic coordinates listed in Table S2 were obtained by a structural analysis based on single-crystal X-ray data, but a reasonable R factor could not be obtained in the analysis because of the diffuse Bragg spots collected from the single crystal ( Figure S1b). The complete Rietveld refinement could not be achieved using the above model, so it was not possible to determine the exact location of the Na atom. However, the large expansion of c suggests that Na is located in the space between MoSe 2 layers. If this is the case, the location of Na at a 2a site may be reasonable because of the presence of a large space around the 2a site. A possible crystal structure of (NH 3 ) y Na x MoSe 2 is shown in Fig. 1c.  (Fig. 2a). The inhomogeneous Na-doping of MoSe 2 may be suggested as its origin. However, as described later, the different x values in (NH 3 ) y Na x MoSe 2 did not provide different T c or T c onset values, which means that the inhomogeneous Na-doping cannot explain the slow decrease. The second possibility is that the (NH 3 ) y Na x MoSe 2 agglomerations shown in Fig. 1a are not single crystals but aggregates of polycrystalline grains because the small size of superconducting grains often results in such a decrease. These possibilities are fully explored later. Powder XRD pattern of (NH 3 ) y Na 0.5 MoSe 2 using synchrotron radiation. 'x' marks correspond to the experimental XRD pattern. Red and green lines refer to calculated patterns (Le Bail fitting) and background, respectively. Ticks refer to the peak positions predicted. In (b), two phases ((NH 3 ) y Na x MoSe 2 and MoSe 2 ) are used in Le Bail fitting. The M/H -T plots in ZFC and FC modes for the (NH 3 ) y Na 0.5 MoSe 2 sample providing the XRD pattern (b) are shown in the inset of (b). (c) Schematic representation of possible (NH 3 ) y Na 0.5 MoSe 2 structure; the structure was drawn based on the atomic coordinates shown in Table S2. As described in the text, this structure may be reasonable if the Na is located in the space between MoSe 2 layers, a possibility supported by the expansion of (c).

Characterization of superconductivity in (NH
The shielding fraction at 2.5 K was 100% for (NH 3 ) 0.4(1) Na 0.41(1) MoSe 2.04(1) ; the shielding fraction was evaluated using the density (ρ = 5.64 g cm −3 ) determined from the above chemical stoichiometry and lattice constants shown in the previous section. Here it should be noted that the above sample was made by Na-doping of an agglomeration of MoSe 2 . As a reference, the M/H -T plot of the (NH 3 ) y Na 0.5 MoSe 2 sample prepared by Na-doping of polycrystalline MoSe 2 powder is shown in Figure S5 of Supplementary Information. The T c and T c onset ( Figure S5) were the same as those (Fig. 2a) of a sample prepared by Na-doping of a MoSe 2 agglomeration, but the shielding fraction was less than 1% at 2.5 K. The behavior of the M/H -T plot below T c onset ( Figure S5) was also the same as that shown in Fig. 2a. These results may show that effective Na-doping can be performed on these agglomerations of MoSe 2 . Moreover, we suggest that the above small fraction (< 1%) may originate in a limiting thickness of superconductivity, i.e., a thin superconducting area formed by metal-doping using polycrystalline MoSe 2 powder. Therefore, throughout this paper, all studies were performed using the samples prepared by metal-doping of agglomerations of MoSe 2 . x was evaluated from the EDX. In (c) the shielding fraction is evaluated using the ρ determined using each chemical stoichiometry for (NH 3 ) y Na x MoSe 2 ; y is assumed to be 0.4. The inset of (c) shows how to determine the T c and T c onset .
Finally, we comment briefly on the Meissner fraction of (NH 3 ) 0.4(1) Na 0.41(1) MoSe 2.04(1) at 2.5 K (shielding fraction = 100% at 2.5 K (Fig. 2a)). The Meissner fraction was approximately 6.7% at 2.5 K which was evaluated from the M/H -T plot in FC mode (Fig. 2a), indicating a small size for superconducting grains. Therefore, this single-crystal like (NH 3 ) 0.4(1) Na 0.41(1) MoSe 2.04(1) may actually consist of polycrystalline superconducting grains, as previously suggested based on the slow drop observed in the M/H -T plot below T c onset (Fig. 2a). However, some of (NH 3 ) y Na x MoSe 2 samples showed a Meissner fraction of more than 20%. Figure S6 shows M/H -T plots of (NH 3 ) y Na 0.5 MoSe 2 exhibiting a Meissner fraction of 25%. Figure 2b shows the M -H curve at 2 K for (NH 3 ) 0.4(1) Na 0.41(1) MoSe 2.04 (1) , which exhibits a clear diamond-like shape. The lower critical field H c1 was determined to be 18 Oe from the expanded M -H curve (inset of Fig. 2b). It was concluded from the M -H curve (Fig. 2b) that the upper critical field, H c2 , was > 0.3 T, indicating a type-II superconductor. Figure S7 shows M/H -T plots at different H's, and the H -T phase diagram ( Figure S7) was constructed from the T c onset at each H; the fitted curve indicates the H c2 at each temperature. The positive curvature seen in Figure S7 is similar to the behavior of (NH 3 ) y K x MoS 2 reported recently 21 . The H c2 at 0 K, H c2 (0), was evaluated to be 2.4 T. However, the data of the H c2 -T c plot are confined near T c . Therefore, the H c2 is shown just for reference. We determined the London penetration depth, λ , to be 520 nm, from H c1 . The shape of the sample was assumed to be isotropic because the measurements of M -H (2 K) and M/H -T at different H's was performed using more than one agglomerations. Figure 2c shows the x dependence of T c in (NH 3 ) y Na x MoSe 2 . The x value was determined from the EDX spectrum, and the x refers to the statistically averaged value with a small error bar falling within the range of the circle (Fig. 2c); the EDX was measured for several areas in one sample. The T c was almost constant (~5 K) with an x-range of 0.4-1. The shielding fraction was higher than 35% in all samples. For the discussion, we plotted T c onset − x in Fig. 2c again because the previous reports on metal-doped MoS 2 and MoSe 2 show the T c onset . The T c onset was also constant (~6 K) in the x-range of 0.4-1. Therefore, we cannot point to an x-dependence of superconductivity in (NH 3 ) y Na x MoSe 2 . Finally, we must comment that the maximum x is 1.0 in (NH 3 ) y Na x MoSe 2 if the Na occupies only a 2a site in the P6 3 /mmc lattice, as described in the subsequent section. To sum up, it must be stressed that the x range must be 0-1 in (NH 3 ) y Na x MoSe 2 . A list of typical superconducting samples is shown in Table 1.
Electronic structure of (NH 3 ) y Na x MoSe 2 . The photoemission spectrum of a single-crystal-like agglomeration of (NH 3 ) y Na 0.5 MoSe 2 measured at 30 K is shown in Fig. 3a; the spectrum was recorded at the Γ point using the Xe-Iα resonance line (8.44 eV). The photoemission intensity was observed on the Fermi level, i.e., the metallic edge was clearly recorded. This shows that (NH 3 ) y Na 0.5 MoSe 2 is metallic in the normal state, and the superconducting transition of (NH 3 ) y Na 0.5 MoSe 2 emerges from the metallic state. The evaluation of the superconducting gap in (NH 3 ) y Na 0.5 MoSe 2 has not yet been done due to the limited resolution of 15 meV in the photoelectron spectrometer, so this is future work. While the metallic edge was clearly observed in the normal state by Xe-Iα light, no signature of the metallic edge was obtained when changing Xe-Iα to the He-Iα resonance line (21.2 eV). We note that the surface of the (NH 3 ) y Na x MoSe 2 single crystal may be oxidized, as the photoemission spectrum using the Xe-Iα resonance line provides more bulk-sensitive results than He-Iα . The successful observation of the metallic edge at the Γ point is fully treated in the Discussion section. Figure 3b,c show the M/H -T curves for (NH 3 ) y Li 0.5 MoSe 2 and (NH 3 ) y K 0.5 MoSe 2 , in ZFC and FC modes. The T c onset and T c were 6.5 and 5.0 K, respectively, for (NH 3 ) y Li 0.5 MoSe 2 , and were 7.5 and 5.3 K for (NH 3 ) y K 0.5 MoSe 2 . The shielding fraction at 2.5 K was 21% for (NH 3 ) y Li 0.5 MoSe 2 , and 10.5% for (NH 3 ) y K 0.5 MoSe 2 . These shielding fractions were roughly estimated using the ρ ( = 6.99 g cm −3 ) of MoSe 2 because the exact ρ could not be determined for (NH 3 ) y Li 0.5 MoSe 2 and (NH 3 ) y K 0.5 MoSe owing to the absence of structural data (lattice constants). Therefore, the values may be slightly overestimated, but the shielding fraction suggests that the superconducting phases can be formed by intercalating alkali metal atoms other than Na. The T c onset s of these materials were higher than the 6 K of (NH 3 ) y Na 0.5 MoSe 2 . However, the T c was almost the same for three (NH 3 ) y M x MoSe 2 's. Furthermore, we synthesized the superconducting (NH 3   shown); the T c was the same as that reported previously 15 . The shielding fraction was ~2.5% at 2.5 K which is lower than those of alkali-metal-doped MoSe 2 .

Superconductivity in other metal-intercalated MoSe 2 .
In the case of (NH 3 ) y M x MoS 2 , the T c onset generally increases with an increase in c 15 , and it increases with the ionic radius (r ion ) of the intercalant. However, the T c onset of (NH 3 ) y Li x MoS 2 deviates from this pattern 15 . The T c onset vs. r ion for (NH 3 ) y M x MoSe 2 (M: Li, Na, Sr and K) is plotted in Fig. 3d, together with that of (NH 3 ) y M x MoS 2 reported previously 15,16 . Similar behavior is seen in the plots of T c onset − r ion of (NH 3 ) y M x MoSe 2 and (NH 3 ) y M x MoS 2 . The T c onset of (NH 3 ) y Li x MoSe 2 deviates from the suggested relationship, as does that of (NH 3 ) y Li x MoS 2 15 . We briefly tried to synthesize (NH 3 ) y M x MoSe 2 (M: Rb, Cs, Ca, Ba, Sr and Yb) as well as (NH 3 ) y Li 0.5 MoSe 2 , (NH 3 ) y Na 0.5 MoSe 2 and (NH 3 ) y K 0.5 MoSe 2 . At the present stage, their superconductivity has not yet been observed, except for (NH 3 ) y Sr x MoSe 2 which was previously reported 15 .

Discussion
Very recently, Shi et al. succeeded in achieving superconductivity through electrostatic electron-doping of MoSe 2 17 . The maximum T c of MoSe 2 reaches 7.1 K at n 2D = 1.69 × 10 14 cm −2 , and the T c can be tuned by the accumulated electron density. The maximum T c is lower than the 10.8 K of MoS 2 11 and the n 2D is higher than the 1.2 × 10 14 cm −2 of MoS 2 11 . For MoSe 2 , a dome-like phase diagram of T c vs. n 2D has not yet been observed because the number of metal-doped MoSe 2 superconductors discovered is still small, i.e., a T c in the n 2D -range (>1.69 × 10 14 cm −2 ), which will be achieved by chemical electron-doping, has not yet been plotted.
A fresh T c − n 2D diagram (Fig. 4a) was prepared using the T c − n 2D plot (electrostatic electron-doping) reported by Shi et al. 17 and the T c − n 2D plot (chemical electron-doping) for (NH 3 ) y M x MoSe 2 samples produced in this study. Here, it should be noted that the 3D electron density, n 3D , evaluated from the x and lattice volume in (NH 3 ) y Na x MoSe 2 was translated to 2D electron density n 2D by assuming the thickness of the channel region to be one layer ( = c/2); the electron concentration donated from a metal atom to the MoSe 2 layer was evaluated assuming that an alkali (alkali-earth) metal atom can donate only one (two) electron, i.e., complex processes such as back-electron transfer to NH 3 were not considered. This is the same method used for the estimation of the T c − n 2D plot for metal-doped MoS 2 17 . In the phase diagram, the T c s of (NH 3 ) y Li 0.5 MoSe 2 , (NH 3 ) y K 0.5 MoSe 2 and (NH 3 ) y Sr 0.261(1) MoSe 2 are also plotted for reference, although the x is an experimental nominal value except , but a continuous change of T c was not obtained in the high n 2D range because of the almost identical T c in metal-doped MoSe 2 prepared in this study (Fig. 4a).
As described in the Results section, the T c onset increases with increasing r ion (Fig. 3d). This behavior is contrary to that of (NH 3 ) y M x FeSe, in which the T c onset is inversely proportional to the r ion 7 . In the case of (NH 3 ) y M x FeSe, the T c is closely associated with the FeSe plane spacing ( = c/2) 7-9 , and elements with a smaller r ion produced larger FeSe plane spacings. This strange behavior can be explained by the fact that the crystal structure differs (off-center or on-center structures) depending on the r ion of the intercalated element 8 , so that (NH 3 ) y Li x FeSe, with an off-center structure, provides a larger FeSe plane spacing and high T c (~44 K) 5,8 . If the T c (or T c onset ) also depends on the MoSe 2 plane spacing in (NH 3 ) y M x MoSe 2 , the graph shown in Fig. 3d implies that an increase in the r ion of the intercalant directly affects the MoSe 2 plane spacing. Actually, the deviation of T c onset of (NH 3 ) y Li 0.5 MoSe 2 and (NH 3 ) y Li 0.5 MoS 2 from the T c onset − r ion curve drawn in the graph shown in Fig. 3d may imply that (NH 3 ) y Li x MoSe 2 adopts a different structure from that (see Fig. 2c) determined for (NH 3 ) y Na x MoSe 2 . In other words, we expect a different location for the Li atom in (NH 3 ) y Li x MoSe 2 than that of the Na atom (probably 2a site), as found in (NH 3 ) y Li x FeSe 6,8 . To sum up, we must discuss the superconductivity of (NH 3 ) y M x MoSe 2 in the light of two variables, n 2D and MoSe 2 plane spacing (or two dimensionality). This makes it difficult to observe a dome-like T c − n 2D phase diagram, as seen from Fig. 4a.
As described in the Results section (Fig. 2c), no x-dependence of T c (or T c onset ) was observed in (NH 3 ) y Na x MoSe 2 . Here, it is very interesting and significant to investigate whether the lattice constants (a,c) change with the x value in (NH 3 ) y Na x MoSe 2 . Figure 4b shows the expanded X-ray diffraction patterns (2θ = 4.0-8.0°), indicating that the 002 peaks due to doped and non-doped phases are observed at the constant 2θ values although the peak intensity due to the doped phase increases monotonically with increasing x in the x-range of 0.35 to 0.86. From this result, it was found that the c does not change with x, suggesting that the stoichiometric (NH 3 ) y Na x MoSe 2 is formed regardless of any increase in x. In other words, the chemical stoichiometry of (NH 3 ) y Na x MoSe 2 does not change even when x increases, and only the fraction of the non-doped phase decreases. Such behavior was recently observed in (NH 3 ) y K x MoS 2 21 , in which the K 0.4 MoS 2 (2H structure) and K 1.0 MoS 2 (1T and 1T' structure) are formed in low and high K concentrations, respectively. The constant T c may be reasonably explained by the scenario that the stoichiometric (NH 3 ) y Na x MoSe 2 compound (or the chemical compound with fixed x and y) is formed in the entire x range, i.e., the stoichiometric x value in (NH 3 ) y Na x MoSe 2 does not change with increasing x as determined from EDX; the EDX estimates the x value including non-intercalated Na atoms. This scenario corresponds to the third possibility described in the Results section.
As seen from Fig. 4b, at higher x values than 0.7, a new peak was observed, indicating the presence of a new c-expanded phase. Figure 4c shows the x-dependence of c in (NH 3 ) y Na x MoSe 2 . From this graph, three different c values are found, due to (1) non-doped pure MoSe 2 , (2) a Na-doped MoSe 2 phase, and (3) another Na-doped MoSe 2 phase with a larger MoSe 2 spacing. Since the T c did not change in the entire x-range regardless of the formation of phase (3), it was unclear whether phase (3) is a new superconducting phase. To sum up, when x increases, two different Na-doped MoSe 2 phases with certain chemical stoichiometry seem to be formed in (NH 3 ) y Na x MoSe 2 . Further study is necessary to clarify the exact stoichiometry of their phases.
Finally, it is necessary to comment on the observation of a metallic edge on the Fermi level in the photoelectron spectrum measured at the Γ point. The band dispersion in bulk crystals of pure MoSe 2 shows an indirect band gap (Γ -(Γ K)) 22 , where (Γ K) means an intermediate state between Γ and K. However, the band dispersion in a single layer of MoSe 2 shows a direct band gap (K -K) 22 . Therefore, a metallic edge for (NH 3 ) y Na x MoSe 2 should be observed at the (Γ K) point for MoSe 2 crystal if we assume a rigid-band picture of band dispersion. Furthermore, even if we assume a single-layer like MoSe 2 accompanied by expansion of the spacing between MoSe 2 layers due to Na-intercalation, a metallic edge must be observed at the K point. Therefore, a metallic edge should not be observed at the Γ point. Nevertheless, a metallic edge was clearly observed in the photoemission spectrum (Fig. 3a). Relevant to this question, it can be observed that the photoemission spectrum must detect all band dispersion of (NH 3 ) y Na 0.5 MoSe 2 since the single crystal of MoSe 2 must be disordered to possess different crystal alignments. In other words, the photoemission spectrum of a polycrystalline-like (NH 3 ) y M x MoSe 2 granule is recorded in Fig. 3a. This interpretation is reasonable since some disorder in the crystal is suggested by the XRD pattern shown in Figure S1b.

Methods
Sample preparation and characterization. Single crystals of MoSe 2 were formed from a polycrystalline powder MoSe 2 sample by physical vapor transport using a furnace with different temperature zones 23 ; the powder MoSe 2 sample was prepared by annealing stoichiometric amounts of Mo and Se at 800 °C for 3 days and 1000 °C for 4 days, according to a procedure reported elsewhere 23 . To form single crystals of MoSe 2 , TeCl 4 was mixed with a MoSe 2 sample as a transport material, the powder MoSe 2 sample was set in the 1000 °C source area, and MoSe 2 single crystals were collected in the low-temperature zone at 900 °C. Here we have used the term 'MoSe 2 single crystal' , but actually it is unclear whether the entirety of an agglomeration consists of one single crystal. Therefore, instead of the term 'single crystal' , it may be valid to use the term 'agglomeration of MoSe 2 ' .
The samples of (NH 3 ) y M x MoSe 2 (M: Na, Li and K) were synthesized by the liquid NH 3 technique as follows: (1) stoichiometric amounts of MoSe 2 agglomerations and an alkali metal were placed in a glass tube, and then NH 3 gas was condensed in the tube. (2) The metal dissolved in the liquid NH 3 at − 60 °C, and the solution (colored blue) was kept below − 50 °C for 6 days. (3) When the color disappeared, the NH 3 was removed by dynamical pumping at room temperature. The same method was used for Sr-intercalation in MoSe 2 .
The DC magnetic susceptibility (M/H) of all samples was measured using a SQUID magnetometer (Quantum Design MPMS2). The single-crystal XRD patterns of the samples were measured with a Rigaku Saturn 724 diffractometer with a Mo Kα source (wavelength λ = 0.71078 Å). The powder XRD patterns of (NH 3 ) y Na 0.5 MoSe 2 and (NH 3 ) y Na x MoSe 2 (x = 0-1) were obtained using synchrotron radiation (λ = 0.4137(1) Å) from the BL10XU beamline and (λ = 0.6887 Å) from the BL12B2 beamline, respectively, of the Spring-8 in Japan; the incident beam was focused by a stacked compound X-ray refractive lens. The samples were introduced into quartz tubes in an Ar-filled glove box for M/H measurements, or into capillaries for XRD; the quartz tubes were pumped and sealed under vacuum, while the capillaries were sealed under Ar atmosphere. The EDX was obtained with an EDX spectrometer equipped with a scanning electron microscope (SEM) (KEYENCE VE-9800 -EDAX Genesis XM 2 ), and the photoemission spectrum with a SCIENTAOMICRON R4000 analyzer and a discharge lamp (SPECS). The Fermi level of the sample was referenced to that of gold, which was in electrical contact with the sample. The sample was cleaved in the ultrahigh-vacuum chamber for the measurement of photoemission spectrum. The photoemission spectrum was measured in an ultrahigh vacuum of ~5 × 10 −9 Pa.