Emergence of superconductivity in (NH₃)_yM_xMoSe₂ (M: Li, Na and K)

Abstract

We report syntheses of new superconducting metal-doped MoSe₂ materials (M_xMoSe₂). The superconducting M_xMoSe₂ samples were prepared using a liquid NH₃ technique and can be represented as ‘(NH₃)_yM_xMoSe₂’. The T_cs of these materials were approximately 5.0 K, independent of x and the specific metal atom. X-ray diffraction patterns of (NH₃)_yNa_xMoSe₂ 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)_yNa_xMoSe₂, indicating the formation of a stoichiometric compound in the entire x range, which is consistent with the x-independence of T_c. 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.

Introduction

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 NH₃ technique have been extensively studied because various superconductors with high superconducting transition temperatures (T_cs) have been discovered^5,6,7,8; the highest T_cs are 46 K at ambient pressure⁵ and 49 K at high pressure⁹. The pressure-induced enhancement of T_c has also been confirmed for non-NH₃ K_xFeSe¹⁰. 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 MoS₂ 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 × 10¹⁴ cm⁻². Also, a signature of 2D superconductivity was observed in electrostatically electron-accumulated MoS₂¹¹. The chemical doping of MoS₂ with alkali and alkaline-earth metal atoms^15,16 provided superconductivity with T_cs lower than the maximum T_c of electrostatically electron-accumulated MoS₂ ^11,12. The chemical doping of MoS₂ was achieved using the liquid NH₃ technique and many superconducting materials have been produced.

Very recently, electron-doping of MoSe₂ was achieved by the electrostatic method¹⁷ and the T_c was precisely tuned in the same manner as in MoS₂. In the case of MoSe₂, only a Sr atom was intercalated and MoSe₂ then showed a T_c as high as 5.0 K¹⁵. This sample was prepared using the liquid NH₃ technique and the chemical composition of Sr_xMoSe₂ can be expressed as ‘(NH₃)_ySr_xMoSe₂’, where the nominal x was 0.2. The shielding fraction of (NH₃)_ySr_0.2MoSe₂ was 60%.

Here, we report syntheses of M_xMoSe₂ samples (M: Li, K and Na) using the liquid NH₃ technique. In this study, Li, Na, K and Sr atoms were intercalated into MoSe₂ solids (only Sr-intercalation had previously been reported)¹⁵. Single-crystal-like agglomerations of (NH₃)_yM_xMoSe₂ (M: Li, Na, K and Sr) were produced. Na-intercalation in (NH₃)_yNa_xMoSe₂ was indicated by its synchrotron powder X-ray diffraction (XRD) pattern. Energy dispersive X-ray spectroscopy (EDX) showed its chemical composition and the amount of NH₃ was also determined from the mass difference before and after reaction. The superconducting parameters were determined from the magnetic field (H) dependence of magnetization (M). The photoemission spectrum at 30 K showed a clear edge on the Fermi level, indicating metallic behavior in the normal state.

Results

Crystal structure of (NH₃)_yNa_xMoSe₂

Single crystals of pristine MoSe₂ were prepared using the annealing technique; details are described in the Methods section. A photograph of a pure MoSe₂ sample is shown in Figure S1a. A single-crystal structure analysis was produced using a piece of MoSe₂ (or single crystal) separated from a MoSe₂ 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 MoSe₂ was included in the single crystal and it was confirmed that no other phase such as Mo₃Se₄ was included. The structure of the MoSe₂ single crystal was hexagonal (space group: No. 194, P6₃/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 MoSe₂¹⁸. Crystallographic data are listed in Table S1. As seen from the magnetic susceptibility M/H (emu g⁻¹ = cm³ g⁻¹) shown in Figure S2, no superconductivity was observed in any precursor MoSe₂ sample, implying no contamination with superconducting Mo₃Se₄. The chemical composition of one MoSe₂ 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 Mo₃Se₄¹⁹, i.e., it was non-superconducting MoSe₂. The EDX spectra, magnetic susceptibilities and single-crystal analyses guaranteed that all MoSe₂ agglomerations used for metal-intercalation throughout this study were in fact substantially ‘MoSe₂’.

Metal-doped MoSe₂ samples were prepared using the liquid NH₃ 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 MoSe₂ was used as the starting material for metal-intercalation. This is based on the successful synthesis of metal-doped FeSe from an agglomeration of FeSe²⁰.

A photograph of (NH₃)_yNa_0.5MoSe₂ prepared using the liquid NH₃ method is shown in Fig. 1a; the stoichiometry of Na (x = 0.5) is an experimental nominal value. The (NH₃)_yNa_0.5MoSe₂ samples (agglomerations) look like single crystals. The EDX spectrum for (NH₃)_yNa_0.5MoSe₂ is shown in Figure S4, which shows that the (NH₃)_yNa_0.5MoSe₂ sample is (NH₃)_0.4(1)Na_0.41(1)MoSe_2.04(1). The amount of NH₃, y = 0.4(1), was determined from the mass difference before and after the reaction that used liquid NH₃. These results indicate that NH₃ 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 NH₃, i.e., which form exists in the MoSe₂ solid? Does it exist as molecular NH₃, 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, (NH₃)_yM_xMoSe₂, is used for convenience because the exact chemical form of NH₃ is unclear.

Figure 1

(a) Photograph of (NH₃)_yNa_0.5MoSe₂ agglomerations. (b) Powder XRD pattern of (NH₃)_yNa_0.5MoSe₂ 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 ((NH₃)_yNa_xMoSe₂ and MoSe₂) are used in Le Bail fitting. The M/H – T plots in ZFC and FC modes for the (NH₃)_yNa_0.5MoSe₂ sample providing the XRD pattern (b) are shown in the inset of (b). (c) Schematic representation of possible (NH₃)_yNa_0.5MoSe₂ 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 MoSe₂ layers, a possibility supported by the expansion of (c).

The structure of (NH₃)_yNa_0.5MoSe₂ (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 MoSe₂ layers, the powder XRD pattern of (NH₃)_yNa_0.5MoSe₂ 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 P6₃/mmc. The sample was prepared from Na and MoSe₂ using the liquid NH₃ 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 MoSe₂, the lattice constants of which are consistent with the values (a = 3.289(7) Å and c = 12.96(3) Å) determined for pure MoSe₂ single crystal in this study. As seen from Fig. 1b, the peak-intensity of 002 peaks for non-doped (minor) and Na-doped MoSe₂ (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 Mo₃Se₄) was found, which is reasonable because the precursor material before metal-doping was demonstrated to be MoSe₂.

The c of 14.810 Å of the main phase is larger by 1.85 Å than that of pure MoSe₂ (12.96(3) Å), indicating that the Na is located in the space between MoSe₂ layers. The a value also increased to 3.541(2) Å from 3.289(7) Å, but the expansion (Δa = 0.252 Å) is too small to be attributed to the intercalation of Na into the MoSe₂ layer. As discussed later, the intercalation of Na at a 2a site, i.e., the space between MoSe₂ 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, NH₃ is not shown. A more precise crystal structure that includes NH₃ must be determined using high-quality (NH₃)_yNa_0.5MoSe₂ 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 MoSe₂ 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 (NH₃)_yNa_xMoSe₂ is shown in Fig. 1c.

Characterization of superconductivity in (NH₃)_yNa_xMoSe₂

Figure 2a shows the M/H – temperature (T) curves in zero field cooling (ZFC) and field-cooling (FC) modes for (NH₃)_0.4(1)Na_0.41(1)MoSe_2.04(1). The T_c^onset and T_c were 6.0 and 5.0 K, respectively, for (NH₃)_0.4(1)Na_0.41(1)MoSe_2.04(1); the T_c was determined from the crossing point of the extrapolation of the normal state and the drop of the M/H – T curve in ZFC mode, as seen from the inset in Fig. 2a. Here, it may be necessary to briefly comment on a small slow decrease in M/H below T_c^onset (Fig. 2a). The inhomogeneous Na-doping of MoSe₂ may be suggested as its origin. However, as described later, the different x values in (NH₃)_yNa_xMoSe₂ 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 (NH₃)_yNa_xMoSe₂ 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.

Figure 2

(a) M/H vs. T plots of the (NH₃)_yNa_0.5MoSe₂ agglomerations in ZFC and FC modes (H = 10 Oe). Inset in (a) shows the method used to determine T_c. (b) M – H curve measured at 2 K for the (NH₃)_yNa_0.5MoSe₂ agglomerations. In the inset of (b), the expanded M – H curve is shown together with the fitted line. The chemical composition of (NH₃)_yNa_0.5MoSe₂ used in (a,b) was determined to be (NH₃)_0.4(1)Na_0.41(1)MoSe_2.04(1) (see text). (c) x-dependence of T_c and T_c^onset in (NH₃)_yNa_xMoSe₂; x was evaluated from the EDX. In (c) the shielding fraction is evaluated using the ρ determined using each chemical stoichiometry for (NH₃)_yNa_xMoSe₂; y is assumed to be 0.4. The inset of (c) shows how to determine the T_c and T_c^onset.

The shielding fraction at 2.5 K was 100% for (NH₃)_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 MoSe₂. As a reference, the M/H – T plot of the (NH₃)_yNa_0.5MoSe₂ sample prepared by Na-doping of polycrystalline MoSe₂ 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 MoSe₂ 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 MoSe₂. 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 MoSe₂ powder. Therefore, throughout this paper, all studies were performed using the samples prepared by metal-doping of agglomerations of MoSe₂.

Finally, we comment briefly on the Meissner fraction of (NH₃)_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 (NH₃)_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 (NH₃)_yNa_xMoSe₂ samples showed a Meissner fraction of more than 20%. Figure S6 shows M/H – T plots of (NH₃)_yNa_0.5MoSe₂ exhibiting a Meissner fraction of 25%.

Figure 2b shows the M – H curve at 2 K for (NH₃)_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 (NH₃)_yK_xMoS₂ reported recently²¹. 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 (NH₃)_yNa_xMoSe₂. 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 MoS₂ and MoSe₂ 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 (NH₃)_yNa_xMoSe₂. Finally, we must comment that the maximum x is 1.0 in (NH₃)_yNa_xMoSe₂ if the Na occupies only a 2a site in the P6₃/mmc lattice, as described in the subsequent section. To sum up, it must be stressed that the x range must be 0–1 in (NH₃)_yNa_xMoSe₂. A list of typical superconducting samples is shown in Table 1.

Table 1 List of representative samples prepared in this study.

Electronic structure of (NH₃)_yNa_xMoSe₂

The photoemission spectrum of a single-crystal-like agglomeration of (NH₃)_yNa_0.5MoSe₂ 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 (NH₃)_yNa_0.5MoSe₂ is metallic in the normal state and the superconducting transition of (NH₃)_yNa_0.5MoSe₂ emerges from the metallic state. The evaluation of the superconducting gap in (NH₃)_yNa_0.5MoSe₂ 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 (NH₃)_yNa_xMoSe₂ 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 3

(a) Photoemission spectrum of (NH₃)_yNa_0.5MoSe₂. M/H versus T plots of (b) (NH₃)_yLi_0.5MoSe₂ and (c) (NH₃)_yK_0.5MoSe₂ agglomerations, respectively, in ZFC and FC modes (H = 10 Oe). (d) Plot of T_c^onset vs. r_ion in (NH₃)_yM_xMoSe₂ and (NH₃)_yM_xMoS₂. Circles and diamonds refer to (NH₃)_yM_xMoS₂ and (NH₃)_yM_xMoSe₂, respectively. The plot is based on the data collected in this study (diamonds) and those in Refs 15 and 16 (circles).

Superconductivity in other metal-intercalated MoSe₂

Figure 3b,c show the M/H – T curves for (NH₃)_yLi_0.5MoSe₂ and (NH₃)_yK_0.5MoSe₂, in ZFC and FC modes. The T_c^onset and T_c were 6.5 and 5.0 K, respectively, for (NH₃)_yLi_0.5MoSe₂ and were 7.5 and 5.3 K for (NH₃)_yK_0.5MoSe₂. The shielding fraction at 2.5 K was 21% for (NH₃)_yLi_0.5MoSe₂ and 10.5% for (NH₃)_yK_0.5MoSe₂. These shielding fractions were roughly estimated using the ρ ( = 6.99 g cm⁻³) of MoSe₂ because the exact ρ could not be determined for (NH₃)_yLi_0.5MoSe₂ and (NH₃)_yK_0.5MoSe 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^onsets of these materials were higher than the 6 K of (NH₃)_yNa_0.5MoSe₂. However, the T_c was almost the same for three (NH₃)_yM_xMoSe₂’s. Furthermore, we synthesized the superconducting (NH₃)_ySr_xMoSe₂ (nominal x = 0.2), which showed a T_c (T_c^onset) as high as 4.8 K (7.0 K) (M/H – T plots not shown); the T_c was the same as that reported previously¹⁵. The shielding fraction was ~2.5% at 2.5 K which is lower than those of alkali-metal-doped MoSe₂.

In the case of (NH₃)_yM_xMoS₂, the T_c^onset generally increases with an increase in c¹⁵ and it increases with the ionic radius (r_ion) of the intercalant. However, the T_c^onset of (NH₃)_yLi_xMoS₂ deviates from this pattern¹⁵. The T_c^onset vs. r_ion for (NH₃)_yM_xMoSe₂ (M: Li, Na, Sr and K) is plotted in Fig. 3d, together with that of (NH₃)_yM_xMoS₂ reported previously^15,16. Similar behavior is seen in the plots of T_c^onset − r_ion of (NH₃)_yM_xMoSe₂ and (NH₃)_yM_xMoS₂. The T_c^onset of (NH₃)_yLi_xMoSe₂ deviates from the suggested relationship, as does that of (NH₃)_yLi_xMoS₂ ¹⁵. We briefly tried to synthesize (NH₃)_yM_xMoSe₂ (M: Rb, Cs, Ca, Ba, Sr and Yb) as well as (NH₃)_yLi_0.5MoSe₂, (NH₃)_yNa_0.5MoSe₂ and (NH₃)_yK_0.5MoSe₂. At the present stage, their superconductivity has not yet been observed, except for (NH₃)_ySr_xMoSe₂ which was previously reported¹⁵.

Discussion

Very recently, Shi et al. succeeded in achieving superconductivity through electrostatic electron-doping of MoSe₂¹⁷. The maximum T_c of MoSe₂ reaches 7.1 K at n_2D = 1.69 × 10¹⁴ 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 MoS₂¹¹ and the n_2D is higher than the 1.2 × 10¹⁴cm⁻² of MoS₂¹¹. For MoSe₂, a dome-like phase diagram of T_c vs. n_2D has not yet been observed because the number of metal-doped MoSe₂ superconductors discovered is still small, i.e., a T_c in the n_2D-range (>1.69 × 10¹⁴ 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 (NH₃)_yM_xMoSe₂ 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 (NH₃)_yNa_xMoSe₂ 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 MoSe₂ 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 NH₃ were not considered. This is the same method used for the estimation of the T_c − n_2D plot for metal-doped MoS₂ ¹⁷. In the phase diagram, the T_cs of (NH₃)_yLi_0.5MoSe₂, (NH₃)_yK_0.5MoSe₂ and (NH₃)_ySr_0.261(1)MoSe₂ are also plotted for reference, although the x is an experimental nominal value except in (NH₃)_ySr_0.261(1)MoSe₂. Consequently, a dome-like phase diagram was suggested in the same manner as MoS₂¹¹, 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 MoSe₂ prepared in this study (Fig. 4a).

Figure 4

(a) Phase diagram of electron-accumulated MoSe₂. This phase diagram is based on the T_c^onset (diamonds) of (NH₃)_yM_xMoSe₂ (this work) and those (circles) of electrostatically electron-accumulated MoSe₂ recently reported by Shi et al.¹⁷ ‘(NH₃)_y’ is omitted in the formulas identifying differently M-intercalated (NH₃)_yM_xMoSe₂. (b) XRD patterns of (NH₃)_yNa_xMoSe₂ samples with different x; each x was determined from the EDX spectrum. The peaks at 2θ = 6.1°, 5.4° and 5.1° correspond to 002 peaks due to non-doped MoSe₂, (NH₃)_yNa_xMoSe₂ and another (NH₃)_yNa_xMoSe₂ phases, respectively. (c) x-dependence of c for the above three phases. The c values do not change with x.

As described in the Results section, the T_c^onset increases with increasing r_ion (Fig. 3d). This behavior is contrary to that of (NH₃)_yM_xFeSe, in which the T_c^onset is inversely proportional to the r_ion⁷. In the case of (NH₃)_yM_xFeSe, the T_c is closely associated with the FeSe plane spacing ( = c/2)^7,8,9 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 element⁸, so that (NH₃)_yLi_xFeSe, 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 MoSe₂ plane spacing in (NH₃)_yM_xMoSe₂, the graph shown in Fig. 3d implies that an increase in the r_ion of the intercalant directly affects the MoSe₂ plane spacing. Actually, the deviation of T_c^onset of (NH₃)_yLi_0.5MoSe₂ and (NH₃)_yLi_0.5MoS₂ from the T_c^onset − r_ion curve drawn in the graph shown in Fig. 3d may imply that (NH₃)_yLi_xMoSe₂ adopts a different structure from that (see Fig. 2c) determined for (NH₃)_yNa_xMoSe₂. In other words, we expect a different location for the Li atom in (NH₃)_yLi_xMoSe₂ than that of the Na atom (probably 2a site), as found in (NH₃)_yLi_xFeSe^6,8. To sum up, we must discuss the superconductivity of (NH₃)_yM_xMoSe₂ in the light of two variables, n_2D and MoSe₂ 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 (NH₃)_yNa_xMoSe₂. Here, it is very interesting and significant to investigate whether the lattice constants (a,c) change with the x value in (NH₃)_yNa_xMoSe₂. 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 (NH₃)_yNa_xMoSe₂ is formed regardless of any increase in x. In other words, the chemical stoichiometry of (NH₃)_yNa_xMoSe₂ does not change even when x increases and only the fraction of the non-doped phase decreases. Such behavior was recently observed in (NH₃)_yK_xMoS₂ ²¹, in which the K_0.4MoS₂ (2H structure) and K_1.0MoS₂ (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 (NH₃)_yNa_xMoSe₂ compound (or the chemical compound with fixed x and y) is formed in the entire x range, i.e., the stoichiometric x value in (NH₃)_yNa_xMoSe₂ 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 (NH₃)_yNa_xMoSe₂. From this graph, three different c values are found, due to (1) non-doped pure MoSe₂, (2) a Na-doped MoSe₂ phase and (3) another Na-doped MoSe₂ phase with a larger MoSe₂ 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 MoSe₂ phases with certain chemical stoichiometry seem to be formed in (NH₃)_yNa_xMoSe₂. 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 MoSe₂ shows an indirect band gap (Γ – (ΓK))²², where (ΓK) means an intermediate state between Γ and K. However, the band dispersion in a single layer of MoSe₂ shows a direct band gap (K – K)²². Therefore, a metallic edge for (NH₃)_yNa_xMoSe₂ should be observed at the (ΓK) point for MoSe₂ crystal if we assume a rigid-band picture of band dispersion. Furthermore, even if we assume a single-layer like MoSe₂ accompanied by expansion of the spacing between MoSe₂ 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 (NH₃)_yNa_0.5MoSe₂ since the single crystal of MoSe₂ must be disordered to possess different crystal alignments. In other words, the photoemission spectrum of a polycrystalline-like (NH₃)_yM_xMoSe₂ 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 MoSe₂ were formed from a polycrystalline powder MoSe₂ sample by physical vapor transport using a furnace with different temperature zones²³; the powder MoSe₂ 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 elsewhere²³. To form single crystals of MoSe₂, TeCl₄ was mixed with a MoSe₂ sample as a transport material, the powder MoSe₂ sample was set in the 1000 °C source area and MoSe₂ single crystals were collected in the low-temperature zone at 900 °C. Here we have used the term ‘MoSe₂ 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 MoSe₂’.

The samples of (NH₃)_yM_xMoSe₂ (M: Na, Li and K) were synthesized by the liquid NH₃ technique as follows: (1) stoichiometric amounts of MoSe₂ agglomerations and an alkali metal were placed in a glass tube and then NH₃ gas was condensed in the tube. (2) The metal dissolved in the liquid NH₃ at −60 °C and the solution (colored blue) was kept below −50 °C for 6 days. (3) When the color disappeared, the NH₃ was removed by dynamical pumping at room temperature. The same method was used for Sr-intercalation in MoSe₂.

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 (NH₃)_yNa_0.5MoSe₂ and (NH₃)_yNa_xMoSe₂ (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 XM₂) 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.