A Boosted Critical Temperature of 166 K in Superconducting D₃S Synthesized from Elemental Sulfur and Hydrogen

Abstract

The discovery of superconductivity in H₃S at 203 K marked an advance towards room‐temperature superconductivity and demonstrated the potential of H‐dominated compounds to possess a high critical temperature (T_c). There have been numerous reports of the H‐S system over the last five years, but important questions remain unanswered. It is crucial to verify whether the T_c was determined correctly for samples prepared from compressed H₂S, since they are inevitably contaminated with H‐depleted byproducts. Here, we prepare stoichiometric H₃S by direct in situ synthesis from elemental S and excess H₂. The Im$\bar{3}$ m phase of D₃S samples exhibits a T_c significantly higher than previously reported values (ca. 150 K), reaching a maximum T_c of 166 K at 157 GPa. Furthermore, we confirm that the sharp decrease in T_c below 150 GPa is accompanied by continuous rhombohedral structural distortions and demonstrate that the Cccm phase is non‐metallic, with molecular H₂ units in the crystal structure.

The $\mathrm{Im}\bar{3}m$ phase of stoichiometric D₃S, synthesized from elemental S and excess D₂ in a diamond anvil cell, exhibits superconductivity with T _c of 166 K at 157 GPa. This is significantly higher than previously reported circa 150 K for samples prepared from disproportionated D₂S.

Room‐temperature superconductivity has been a long‐standing endeavor in the fields of physics and material science. According to the Bardeen–Cooper–Schrieffer theory of superconductivity,1 high phonon frequencies and strong electron–phonon interactions are favorable for a high T _c, and hydrogen naturally appears as the best candidate.2 Although the formation of a metallic phase was recently reported,3 experimental evidence of superconductivity in hydrogen remains a major challenge, since it requires pressures of about 500 GPa.4 To decrease the pressure of metallization in pure hydrogen to accessible values, Ashcroft has suggested chemical precompression with heavier atoms.5

While Group 4 hydrides, which were originally proposed for doped hydrogen, did not succeed, superconductivity was observed near 200 K in compressed H₂S at about 150 GPa;6 these correlate with independent predictions for H₃S compositions with the same high T _c.7 Correlation between the observed superconductivity and proposed $\mathrm{Im}\bar{3}m$ crystal lattice for H₃S was found experimentally shortly thereafter.8 There have been several theoretical and experimental studies of the H‐S system.9 However, several questions remain unanswered. In particular, it is important to confirm whether T _c values were determined reliably for their particular superconducting phases, and to elucidate which phase of H₃S stoichiometry is responsible for the sharp decrease in T _c below 150 GPa.

Because Drozdov et al.6b used H₂S as a starting compound, guided by predicted superconductivity in H₂S at 70 K,10 questions regarding the purity of samples arose from the very beginning. Indeed, $\mathrm{Im}\bar{3}m$ H₃S can be prepared by disproportionation of H₂S.6b, 8, 11 However, such samples are likely contaminated by a H‐depleted phase. Although predictions suggest that the only thermodynamically stable byproduct of the reaction is pure S above 113 GPa,12 experimental X‐ray diffraction data indicate a complex composition: S content varies in different samples and is always smaller than expected, even at higher pressures of 140–190 GPa.8, 11, 12, 13 The persistence of H₂S and H₄S₃ in samples at pressures above 140 GPa indicates that large kinetic barriers suppress decomposition.12

The highest measured T _c for such samples is 203 K at 155 GPa in H₃S and 152 K at 173 GPa in D₃S.6b, 9a, 13a T _c values for different samples6b, 8, 9a are highly disperse (ca. 15 K), indicating poor crystallinity, inhomogeneity, and impurities in the superconducting phase. These imperfections can lower T _c compared to those observed with the ideal $\mathrm{Im}\bar{3}m$ phase.

Guigue et al.14 and Goncharov et al.15 demonstrated that H₃S compounds of better crystallinity could be prepared via direct chemical synthesis from S and H₂. This approach yielded products without H‐depleted impurities, since H₂ was used in excess. Electrical measurements for the directly synthesized $\mathrm{Im}\bar{3}m$ phase of H₃S revealed T _c values of about 200 K at about 150 GPa.16 However, neither the pressure‐dependence of T _c, nor data for the deuterium counterpart were reported.

Herein, we report a systematic study of compounds with H₃S and D₃S stoichiometry synthesized directly from laser‐heated mixtures of S and excess H₂ (D₂). We present an enhanced T _c of 166 K for the $\mathrm{Im}\bar{3}m$ phase of D₃S, evaluate the phase diagram of H₃S (D₃S) over the wide pressure range of 110–170 GPa, and discuss the electrical properties of the Cccm, R3m, and $\mathrm{Im}\bar{3}m$ phases.

At high pressures, S reacts readily with H₂ giving final products with H₃S stoichiometry. The formation of particular phases depends on the pressure at which the sulfur–hydrogen mixture is heated. At 111–132 GPa, the mixture yields the Cccm phase (samples 1–3) even with subtle laser‐heating at 700–1000 K, whereas the $\mathrm{Im}\bar{3}m$ phase requires pressures over 150 GPa and temperatures of 1500–2000 K (samples 4–6). In total, three H₃S and three D₃S samples were synthesized. The conditions for each in situ synthesis and the pressure ranges at which samples were studied are summarized in Figure 1 and Experimental Section (Supporting Information).

Figure 1.

Synthesis of H₃S and D₃S from elemental S and H₂ (D₂). a) The conditions for laser‐heating induced synthesis and the pressure ranges at which samples 1–6 were studied. Vertical arrows show the pressures at which the pulse laser was applied: heating initiates either the chemical reaction between S and H₂ (D₂) or the R3m‐to‐Cccm phase transition in D₃S. Black and red arrows correspond to the H‐S and D‐S systems, respectively. Horizontal dotted arrows show the pressure range over which the synthesized samples were studied. Colored boxes define the pressure ranges for the different phases. b) Photograph of sample 3 in the diamond anvil cell (DAC). At the top, a rectangular piece of S surrounded by D₂ is clamped in the round cavity in the insulating transparent gasket at 132 GPa. Two lower photographs demonstrate the formation of the Cccm phase of D₃S resulting from a chemical reaction after two successive laser treatments to about 700–800 K. c) Illustration of the diamond anvil assembly for the four‐probe electrical measurements at high pressures.

The Cccm phase is sustainable with further compression. Increasing the pressure to 152 GPa with subsequent laser heating does not initiate the phase transition to the more energetically favorable $\mathrm{Im}\bar{3}m$ or R3m phases. The presence of the Cccm phase at significantly higher pressures than the predicted upper limit of about 100 GPa7 has also been observed earlier14, 15 and indicates an extended metastable region for this phase.

The crystal structure and properties of the $\mathrm{Im}\bar{3}m$ and Cccm phases differ dramatically (Figure 2). The $\mathrm{Im}\bar{3}m$ phase is a metal with a strong metallic luster and a small resistance of <0.5 Ω at room temperature, whereas the Cccm phase is an insulator with an electrical resistance of about 10⁶ Ω that does not decrease with cooling or compression. Refined crystal structures from XRD data for sample 1 and sample 4 agree with the theoretical Cccm and $\mathrm{Im}\bar{3}m$ structural models, respectively.7

Figure 2.

Structural data for H₃S samples synthesized from S and H₂. a) Rietveld refinement for the Cccm phase of H₃S at 118 GPa (sample 1), and b) $\mathrm{Im}\bar{3}m$ phase of H₃S at 155 GPa (sample 4). Minor peaks in (b) originating from the β‐Po phase of sulfur and the gold leads marked as blue and red dashes, respectively. Photos of the corresponding samples are shown on the upper‐right corner. c) Typical Raman spectra for the Cccm phases of H₃S and D₃S at high pressures: the blue spectrum corresponds to pure sulfur after metallization (sample 5 at 115 GPa); black and red spectra correspond to the Cccm phases of H₃S in the heated sample 2 at 128 GPa and D₃S in the heated sample 3 at 132 GPa, respectively. Black arrows show the redshift in the H−H and S−H stretching vibrations after isotopic substitution. d),e) Fragments of the refined crystal structures for the Cccm and $\mathrm{Im}\bar{3}m$ phases of H₃S (H atoms were put in calculated positions7 and not refined). S and H atoms are shown as yellow and gray spheres, respectively; molecular H₂ units in the orthorhombic lattice are blue.

In contrast to the Raman‐inactive metallic $\mathrm{Im}\bar{3}m$ phase of H₃S (D₃S), the Cccm phase has very strong Raman‐active modes. Spectroscopic data can be used to extract valuable information about the H‐sublattice, which cannot be derived from XRD data. Isotopic substitution within the Cccm phase results in a redshift of about $\sqrt{2}$ for those Raman modes associated with vibrations involving H atoms. A broad Raman band for sulfhydryl groups at 2500 cm⁻¹ in H₃S and at 1860 cm⁻¹ in D₃S indicates the presence of strong S−H⋅⋅⋅S H‐bonds in the crystals.17 Two bands, at 3720 and 3875 cm⁻¹ in H₃S, and at 2735 and 2840 cm⁻¹ in D₃S, are assigned to H‐H_str and D‐D_str from the coordinated H₂ and D₂ molecular units in the Cccm phase, respectively (Figure 2 c).

Compared to the Raman bands at 4010 cm⁻¹ for H−H_str and 3010 cm⁻¹ for D−D_str, observed for bulk H₂ (D₂) media around the H₃S (D₃S) samples, the redshift in the Cccm phase indicates a strengthened interaction between the H₂ (D₂) molecules and the rigid crystal framework. These data confirm the theoretical structural model for the Cccm phase of H₃S,7 which contains two crystallographically nonequivalent H₂ molecular units (Figure 2 d). According to the model, the first type of H₂ in the lattice has a shorter H−H bond length and longer contacts to the closest S atoms, whereas the second type has a longer H−H bond and a shorter distance to the surrounding atoms. These predictions agree with the spectroscopic data: stronger coordination of molecular units of the second type causes increased elongation of the H−H bond and, therefore, a larger redshift for the H−H_str band in the Raman spectra.

Samples with the $\mathrm{Im}\bar{3}m$ phase of H₃S (D₃S) demonstrate high T _c values at pressures ranging 150–170 GPa (Figure 3). Sample 4, for instance, has a T _c of 196 K at 148 GPa (Figure 3 b). Owing to better sample crystallinity, the superconductive transitions are sharper and narrower than those reported for samples prepared from compressed H₂S (D₂S).6b, 8 Recently published data for the $\mathrm{Im}\bar{3}m$ phase of H₃S synthesized from S and H₂ also demonstrate similar T _c values of about 200 K at about 150 GPa.16 In summary, among numerous samples prepared from compressed H₂S,6 the highest observed T _c values compare well to values measured for samples synthesized from the elements.

Figure 3.

Four‐probe electrical measurements for the superconducting phases of the synthesized H₃S and D₃S samples at high pressures. a) Temperature‐dependence of electrical resistance for the $\mathrm{Im}\bar{3}m$ phases of H₃S (sample 4, black) and D₃S (sample 5, orange; and sample 6, red) near 155 GPa. The absolute resistance values for samples 4 and 6 were divided by 4 and 23, correspondingly, for presentation. The green horizontal line is a guide for zero resistance. b) Summarized temperature dependence for the T _c observed in electrical measurements for different superconducting H₃S (black symbols) and D₃S (red symbols) samples reported to date. Data collected for H₃S and D₃S samples prepared from compressed H₂S and D₂S are shown as open symbols.6b, 8, 9a Data for H₃S samples synthesized earlier from S and H₂ are shown as blue circles.16 Data measured in the present study are shown as black, red, and orange circles (consistent with coloring for samples 4, 5, and 6 in Figure 3 a). Red circles with black frames correspond to sample 6 on subsequent compression from 140 to 150 GPa. The white and blue regions define the pressure ranges where the R3m and $\mathrm{Im}\bar{3}m$ phases of H₃S and D₃S are stable.

In contrast to H₃S, the deuterium analogue demonstrates a significantly enhanced T _c, reaching a record 166 K at 157 GPa in sample 5 and 164 K at 161 GPa in sample 6. These values agree well with the predicted T _c of 159 K obtained from assumptions that the isotope effect is independent of pressure.18 Thus, the T _c for cubic D₃S synthesized from S and D₂ significantly exceeds, by about 15 K (or ca. 10 %), the maximum value of 152 K measured previously for samples prepared via pressure‐induced disproportionation of D₂S.6, 8 The lower T _c values in such samples were likely caused by inferior crystallinity, inhomogeneity of the $\mathrm{Im}\bar{3}m$ phase, contamination by D‐depleted byproducts, and impurity of the initial D₂S source (97 %).6b

Further compression of the $\mathrm{Im}\bar{3}m$ phase leads to a decrease in T _c to 194 K at 155 GPa for H₃S (sample 4) and to 163 K at 170 GPa for D₃S (sample 6). This behavior agrees with data for samples prepared from H₂S (D₂S)6b and is provoked by pressure‐induced hardening of the phonon frequencies.19

Using the newly obtained data for T _c values in H₃S at 155 GPa and D₃S at 157 GPa, we calculated the isotope effect coefficient, α=−(lnT _c ^D3S−lnT _c ^H3S)/(lnM ^D−lnM ^H), where M ^D and M ^H are the atomic masses of D and H, respectively. The refined α for the $\mathrm{Im}\bar{3}m$ phase is ≈0.22, substantially smaller than both the value of about 0.42 derived from T _c values for disproportionated H₂S (D₂S)6b and the expected canonical BCS value of 0.5. The low value of α likely stems from anharmonic effects.

Indeed, according to isotropic Migdal–Eliashberg equations, the calculated T _c for the $\mathrm{Im}\bar{3}m$ phase of H₃S is 250 K; T _c decreases significantly to 194 K if anharmonic effects are considered.20 The computed T _c for the anharmonic case agrees well with the measured values. However, the same calculations for D₃S contradict the experiment and give 183 K and 152 K for harmonic and anharmonic approximations, respectively.20

Next, we discuss dramatic changes in superconducting properties accompanying the $\mathrm{Im}\bar{3}m$ ‐to‐R3m phase transformation. Decreasing pressure causes an abrupt drop in T _c to 93 K at 140 GPa for D₃S. Similar behavior is observed for samples prepared from compressed D₂S.6b, 9a, 19c This trend is reversible and T _c is restored if pressure increases again (Figure 3). The decrease in T _c for D₃S is accompanied by structural changes. On decompression, the $\mathrm{Im}\bar{3}m$ phase becomes instable and is distorted, decreasing the lattice symmetry to R3m. These rhombohedral distortions are more pronounced than previously predicted:7 further to a subtle reorientation of the H‐sublattice and desymmetrization of the S−H−S bonds, the heavier S‐sublattice also loses cubic symmetry. Changes in the S‐sublattice manifest as splitting of the cubic phase reflections in X‐ray powder patterns (Figure 4). This phase transition was not detected for samples prepared from H₂S (D₂S), likely because of broad reflections stemming from poorly crystallized H₃S (D₃S) compounds,8, 11 but splitting was reported in the 110 and 211 reflections of the cubic phase for samples synthesized from S and H₂ (with improved crystals).15 The drastic rearrangement of the crystal structure also manifests in the Raman spectrum for the R3m phase of D₃S, with two strong and narrow bands at 350 and 370 cm⁻¹ and a composite broad band at 900–1100 cm⁻¹ (Figure 4 d). The metallic properties change as well; the sample loses metallic luster and its resistance increases. Annealing at about 1500 K and 140 GPa converts the structure from the R3m into the Cccm phase (Figure 4 c).

Figure 4.

Transformation of the $\mathrm{Im}\bar{3}m$ phase of D₃S to the R3m and Cccm phases on decompression of sample 6. a) Rietveld refinement for the $\mathrm{Im}\bar{3}m$ phase after heating the S and D₂ mixture at 161 GPa, b) the R3m phase after decreasing the pressure to 140 GPa, and c) the Cccm phase after subsequent heating to about 1500 K at 140 GPa. d) Raman spectra of sample 6 on decompression. The orange spectrum corresponds to the R3m phase of D₃S at 140 GPa, illustrated in (b). The broad band at 900–1200 cm⁻¹ is fitted by four single modes. e) The reversible change in resistance for the R3m and $\mathrm{Im}\bar{3}m$ phases of D₃S at room temperature on decompression (open circles) and pressurizing (filled circles). f)–h) Photographs of sample 6 taken under reflected illumination at decreasing pressure: f) the $\mathrm{Im}\bar{3}m$ phase at 161 GPa, g) the R3m phase at 140 GPa, and h) the Cccm phase of D₃S at 140 GPa. Metallic luster reduces after each phase transition.

These data clarify the phase diagram for H₃S (D₃S) and provide strong evidence that the R3m phase is an intermediate metastable phase. The R3m phase appears only on decompression, when the cubic phase is already instable, but the phase transition to the thermodynamically more stable Cccm phase is hindered by kinetic barriers. Taking structural features into account, the activation energy for the Cccm‐to‐$\mathrm{Im}\bar{3}m$ phase transition should contain not only the energy required for the crystal lattice rearrangement, but also the energy needed to dissociate H₂ molecular units in the crystal. In fact, experimental data support the high activation energy value. The Cccm phase survives increasing pressures up to at least 160 GPa,14 and the distorted cubic phase (R3m) persists on decompression at least down to 70 GPa, at which point only heating the sample to 1300 K triggers the transition to the Cccm phase.15

This new insight into the phase diagram for H₃S (D₃S) explains why Drozdov et al. were able to produce samples with high T _c values from H₂S via low‐temperature compression and annealing above 150 GPa. The superconducting phases of the H₃S composition could not be synthesized by annealing pressurized samples with H₂S below 150 GPa, since the only thermodynamically stable phase of H₃S at these pressures is Cccm. Neither could they be prepared by continuous compression of H₂S at room temperature, because the measured T _c values for such samples never exceed 80 K (or 40 K for the D‐S system), even at higher pressures up to 190 GPa.6 Low‐temperature pressurizing prevented chemical decomposition and disproportionation of H₂S, allowing it to exist at pressures at which the $\mathrm{Im}\bar{3}m$ phase of H₃S is thermodynamically stable.

In summary, we synthesized stoichiometric H₃S and D₃S from elemental S and excess H₂ (D₂) at 111–161 GPa and refined the phase diagram for the Cccm, $\mathrm{Im}\bar{3}m$ , and R3m phases of H₃S (D₃S). We revealed that the synthesized $\mathrm{Im}\bar{3}m$ D₃S samples exhibit reproducible increased T _c values of up to 166 K at 157 GPa and confirmed that continuous distortions of the cubic phase into the R3m phase cause a sharp decrease in T _c below 150 GPa. Moreover, we demonstrated that the Cccm phase is non‐metallic, with molecular H₂ (D₂) units in the crystal structure.

Conflict of interest

The authors declare no conflict of interest.

Supporting information

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Supplementary

V. S. Minkov, V. B. Prakapenka, E. Greenberg, M. I. Eremets, Angew. Chem. Int. Ed. 2020, 59, 18970.