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# Superconductivity above 200 K discovered in superhydrides of calcium

## Abstract

Searching for superconductivity with Tc near room temperature is of great interest both for fundamental science & many potential applications. Here we report the experimental discovery of superconductivity with maximum critical temperature (Tc) above 210 K in calcium superhydrides, the new alkali earth hydrides experimentally showing superconductivity above 200 K in addition to sulfur hydride & rare-earth hydride system. The materials are synthesized at the synergetic conditions of 160~190 GPa and ~2000 K using diamond anvil cell combined with in-situ laser heating technique. The superconductivity was studied through in-situ high pressure electric conductance measurements in an applied magnetic field for the sample quenched from high temperature while maintained at high pressures. The upper critical field Hc(0) was estimated to be ~268 T while the GL coherent length is ~11 Å. The in-situ synchrotron X-ray diffraction measurements suggest that the synthesized calcium hydrides are primarily composed of CaH6 while there may also exist other calcium hydrides with different hydrogen contents.

## Introduction

Superhydrides have received growing attentions recently because of high temperature superconductivity (SC)1. It was suggested that superhydrides are likely to be a step toward metallic hydrogen since the “chemically precompressed” hydrogen in the superhydrides can decrease the critical pressure required for the metallization1,2,3. Because of high phonon frequencies and strong electron-phonon coupling, high temperature SC was suggested in hydrogen rich materials. Sulfur hydride is one of example in which the high Tc SC was reported both theoretically & experimentally at megabar level pressures4,5. In addition, alkali-earth, rare-earth, and other superhydrides are theoretically suggested to possibly possess high temperature SC at high pressures6,7,8,9,10,11. Those metal superhydrides favor to form hydrogen rich coordination such as clathrate-like cage structures at high pressure where the metal ions are located in the center of the H clathrates and act as carrier donor. The occupation of the unfilled anti-bonding σ* orbitals of the H2 molecules by the electrons from the metal ions would enhance to dissociate the H2 molecules hence form H clathrates. Since the discovery of SC in sulfur hydrides, other superhydrides have been experimentally reported to have SC, including LaH1011,12,13,14, YH98,15, CeH916, ThH1017, zirconium polyhydrides18, tin hydrides19, YH420, and LuH321 etc.

Although alkali-earth superhydrides were predicted to have high temperature SC, so far there are no experimental observations for SC above 200 K, in spite of SC with Tc ~20 K was reported in barium hydrides22. Here, we report the experimental discovery of high Tc SC in calcium superhydrides synthesized at high pressure and high temperature conditions. The SC with Tc ~210 K at 160 ~190 GPa was observed. Hence in addition to sulfur hydrides and rare-earth hydrides, this is a new alkali-earth hydride superconductor with Tc above 200 K.

## Results and discussions

### High-temperature superconductivity

Figure 1a displays the image of the sample assembly. The dotted red square is the sample shape and the four gray dotted regions are the inner electrodes composed of Pt. Figure 1b shows the measurements of resistance as function of temperature at 160 GPa for Sample A. The resistance curves almost coincide for both the cooling and warming cycles. The resistance drops at around 210 K and approaches to zero at low temperature, suggesting that the superconducting like transitions take place in the calcium superhydrides. Figure 2 shows the resistance measurements by application of magnetic fields for Sample A. It is seen that the whole transition curves shift to low temperature with the critical temperature gradually suppressed by the applied field, consistent with the nature of superconductivity. The inset of Fig. 1b displays an enlarged view of the derivative of resistance over temperature around the transition region, from which the Tconset of 210 K is estimated referring to right side upturn point. The experimentally observed Tc value of 210 K is comparable to the theoretical predictions for the calcium hydride CaH6 that crystalizes in a cubic structure with the space group of Im-3m6.

In addition to the first transition at ~210 K, there are also several drop kinks at ~180 K and ~160 K as shown in Fig. 1b. These drop kinks imply multistep superconducting transitions that are supported by the broaden transition curves shown in Fig. 2. In the context of theoretical calculation, the calcium hydrides such as CaH6, CaH12 etc are predicted to have high Tc SC at high pressure2,6. Since near the experimental pressure of 160 GPa, CaH4, CaH6, and CaH12 are predicted to be stable, the stoichiometric ratio of the synthesized superconducting hydrides CaHx should be mainly determined by the hydrogen content released during the laser heating process. Hence it is likely that these multistep transitions should be attributed to calcium hydrides with different hydrogen amounts, which are probably due to inhomogeneous hydrogen distribution.

To increase homogeneity of the generated hydrogen, more homogenous scanning heating manner controlled by computer was adopted. We performed several sample synthesis to achieve a single superconducting phase transition by optimizing pressure and temperature conditions. Figure 3a presents the resistance for Samples B and C as function of temperature measured at 185 GPa, where a sharp superconducting transition is achieved. The SC is supported by the measurements at applied magnetic field as shown in Fig. 3b. For the Sample D, the superconducting transition is shown in Supplementary Fig. 1. Thus, our results show the experimental discovery of high temperature superconducting alkali earth superhydride with Tc exceeding 200 K, joining the 200 K above superhydrides of SH3 and LaH10 and YH9. Since hydrogen is the lightest element, superhydrides are expected to have high Debye temperature and thus possible high Tc SC according to the prediction by conventional BCS theory. In addition, for the reported binary superhydrides with high Tc SC, it was found that most of elemental metals are on the boundary of s and d blocks in the elemental period table2, such as La in LaH10 and Y in YH9. For these elemental metals, electrons can be transferred from filled s orbital to d orbital under high pressure due to the small energy difference between these orbitals, which usually increases the structural instability and enhances the electron-phonon coupling strength and thus leads to possible SC with high Tc as well2,23,24. The Ca lattice in CaH6 predicted in ref. 6 is highly compressed under high pressure, which suggests the possible large electron phonon coupling strength caused by the electron s-d orbital transfer. Therefore, the combination of the high Debye temperature and the large electron-phonon coupling strength makes it possible to reach high Tc SC in calcium superhydrides.

### Physics parameters measurements

To estimate the upper critical field Hc2(0), the superconductivity as a function of magnetic field was investigated based on Sample C. The Tc values are determined with the criteria of the Tconset, the temperature at 90 and 50% of normal state resistance (Tc90% and Tc50%), respectively. By linear fitting the Hc2 (T), the slope of dHc2/dT|Tc was obtained to be −1.976 T/K for Tconset, −1.726 T/K for Tc90%, and −1.389 T/K for the Tc50%. Using the Werthamer-Helfand-Hohenberg (WHH) formula of $${{\mu }_{0}H}_{c2}\left(T\right)=-0.69\times {{dH}}_{c2}/{dT}{{{{{{\rm{|}}}}}}}_{{Tc}}\times {T}_{c}$$, the Hc2(0) value was calculated to be 268T, 226T, and 180T for the criteria of Tconset, Tc90%, and Tc50%, respectively. The Ginzburg Landau (GL) formula of $${{\mu }_{0}H}_{c2}\left(T\right)={{\mu }_{0}H}_{c2}\left(0\right)(1-{(T/{T}_{c})}^{2})$$ is also used to estimate the upper critical field at zero temperature. As shown in Fig. 4 the fitting of the μ0Hc2(T) by GL formula gives a value of Hc2(0) ranging from 131T to 196T using criteria of Tconset, Tc90% and Tc50%, respectively. These are comparable to values reported for LaH1012. Using the obtained value of Hc2(0) = 131–268 T, one can roughly estimate the GL coherence length ξ to be 11–16 Å via the equation of μ0Hc2(0) = Φ0/2πξ2, where Φ0 = 2.067 × 10−15 Web is the magnetic flux quantum.

### Structure characterizations

The possible superconducting phases are investigated by high pressure X-ray diffraction experiments. Supplementary Fig. 2a shows the room temperature X-ray diffraction pattern for a synthesized sample, where the Im$$\bar{3}$$m phase of CaH6 was indexed. Supplementary Figure 2b shows the X-ray diffraction patterns measured at various high pressures starting from the synthesized pressure up to 243 GPa where the anvils were broken. The pressure dependence of unit cell volume of the CaH6 is presented in Fig. 5. By using the Birch–Murnaghan Eq. (1),

$$P\left({{{{{\rm{GPa}}}}}}\right)= \, \frac{3}{2}\times {B}_{0}\left[{\left(\frac{{V}_{0}}{V}\right)}^{\frac{7}{3}}-{\left(\frac{{V}_{0}}{V}\right)}^{\frac{5}{3}}\right]\\ \times \left\{1-\left(3-\frac{3}{4}\times {B}_{0}^{{\prime} }\right)\times \left[{\left(\frac{{V}_{0}}{V}\right)}^{\frac{2}{3}}-1\right]\right\}$$
(1)

where B0 is the bulk modulus and B0’ is the pressure derivative bulk modulus, the P-V data are fitted and B0 is estimated to be about 221 GPa at B0′ = 3. From the fit of equation of state the lattice constant a at 150 GPa is estimated to be 3.308 Å, which is close to that predicted by theoretical calculation. This suggests that the superconducting sample contains Im$$\bar{3}$$m phase of CaH6. However, other phase(s) might be mixed since there are some unknown weak peaks in the diffraction patterns. We became aware during preparing the paper that an independent work by Ma et al. was carried with the similar results25.

In summary high Tc calcium superhydrides superconductors are discovered with critical temperature Tc above 210 K at pressures ~160 GPa. The upper critical field Hc(0) was estimated to be ~268T that corresponds to ~11 Å coherent length in GL model for the calcium superhydride superconductor. The results show that calcium superhydrides are new type hydrogen rich superconducting compounds with transition temperature above 200 K in addition to sulfur hydride & rare-earth hydride system.

## Methods

### High pressure assembly

Diamond anvil cell techniques are used for both synthesis and measurements of the calcium hydrides. The diamond anvils are of optical pure quality with culet diameter of 100 μm beveled to 300 μm for the experiments. The electrodes for resistance measurements are embedded in the sample chamber before high pressure and high temperature synthesis. The experiments are conducted in two steps: (I) synthesis of the calcium hydrides at high pressure and high temperature; (II) the follow up measurements of SC for the sample quenched from high temperature but remained at the same pressure. The T301 stainless steel served as gaskets that are prepressed from 250 μm to ~20 μm in thickness at ~20 GPa. A hole of 300 μm in diameter was drilled at the center of imprint, and was filled with fine insulating cubic boron nitride (cBN) powder mixed with epoxy that was pressed with anvils to form a solid layer of ~15 µm in thickness. A hole of 70 μm in diameter was drilled at the center of the solid cBN layer to serve as the sample chamber. The Pt foils with a thickness of 0.5 μm were deposited on the surface of the culet as the inner electrodes. Gold wire was attached to the Pt foil to serve as the outside electrodes. High purity calcium metal (99.9%) was adopted as precursor material: a 2-μm thick calcium specimen with dimensions 30 μm × 30 μm was stacked on the inner electrodes. A flake of ammonia borane was inserted into the sample chamber to act as a hydrogen source (hydrodizer) while also serving as the pressure transmitting medium14. The sample loading as well as electrodes deposition were conducted in a glove box filled by flowing Ar gas with 1 ppm less trace water or oxygen to avoid moisture or contamination. The diamond anvil cell was then clamped in the glove box before the measurements. The described setup followed the ATHENA procedure reported ref. 26.

### Sample synthesis and resistance measurements

A piston cylinder type anvil cell composed of BeCu was adopted in the experiments. The sample was first pressed to 160–190 GPa followed by heating at ~2000 K for ~6 min. The heating was performed with a pulse laser beam of 1064 nm wavelength. The laser had a focused spot size 5 μm in diameter with a power of 20 W. The heating temperature was estimated by fitting the black body irradiation spectra. A computer controlled scanning heating method was adopted to increase the homogeneity of the generated hydrogen. The heated sample was then quenched from high temperature while held at high pressure. The synthesized sample compressed within diamond anvil cell was put into a MagLab system to perform the electric conductivity measurements using a Van der Pauw method with 1 mA applied current. The MagLab system can provide synergetic extreme environments with temperatures from 300 K to 1.5 K and a magnetic field up to 9T27,28. Pressure was calibrated by the shift of the first order Raman edge frequency from the cutlet of diamond29.

### High pressure x-ray diffraction measurements

The synchrotron X-ray diffraction experiments in the diamond anvil cell are carried out at GSECARS of the Advanced Photon Source at the Argonne National Laboratory. X-ray with λ = 0.3344 Å are focused down to ~3 μm diameter spot on the sample. A symmetric diamond anvil cell was used to generate pressure with beveled diamond anvils (100/300 μm) and a rhenium gasket indented to 25 μm. Samples are loaded into the pressure chamber without cBN insulating layer. Calcium hydrides are synthesized in situ at 190 GPa with laser heating at 2000 K. The sample pressure in the synchrotron X-ray diffraction experiments was determined by both the shift of Raman edge frequency from the cutlet of diamond and the equation of state for rhenium. The X-ray diffraction images are converted to one dimensional diffraction data with Dioptas30.

## Data availability

All the data generated in the study are available upon reasonable request to the corresponding author.

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## Acknowledgements

The work is supported by NSF, MOST, and CAS of China through research projects. Portions of this work were performed at GeoSoilEnviroCARS (The University of Chicago, Sector 13), Advanced Photon Source (APS), Argonne National Laboratory. GeoSoilEnviroCARS is supported by the National Science Foundation–Earth Sciences (EAR–1634415) and Department of Energy-GeoSciences (DE-FG02-94ER14466). This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. We are grateful to Prof. J.G. Cheng, J.P. Hu, and L. Yu for the discussions. We thank Prof. T. Xiang, B.G. Shen, and Z.X. Zhao for the consistent encouragements.

## Author information

Authors

### Contributions

Research design, coordination & supervision: C.Q.J.; high-pressure synthesis and in situ resistance measurements: Z.W. L., X.H., C.L.Z., S.J.Z., Y.T.J., S.M.F., Y.W.L., X.C.W., J.Z., B.S.M., R.C.Y, J.F.Z., and C.Q.J; in situ synchrotron experiments: L.H.W., M.Y.Y., Z.S.Z., V.B.P., S.C., P.A.G., J.B., S.H.Y., and H.Z.L., manuscript writing: Z.W.L., X.C.W., and C.Q.J. All authors contributed to the discussions.

### Corresponding authors

Correspondence to Xiancheng Wang or Changqing Jin.

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The authors declare no competing interests.

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Li, Z., He, X., Zhang, C. et al. Superconductivity above 200 K discovered in superhydrides of calcium. Nat Commun 13, 2863 (2022). https://doi.org/10.1038/s41467-022-30454-w

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• DOI: https://doi.org/10.1038/s41467-022-30454-w