Advances in the Synthesis and Superconductivity of Lanthanide Polyhydrides Under High Pressure

Room-temperature superconductors have long been the ultimate goal of scientists. Pressure-stabilized hydrides are a new rapidly growing class of high-temperature superconductors and are believed to be a new superconducting system, undoubtedly leading to a surge in the discovery of new hydrogen-rich materials. They are the forefront of physics and material science. Lanthanide polyhydrides formed under pressure are promising conventional superconductors. Especially, both the theoretical and experimental reports on lanthanum superhydrides under pressure, exhibiting superconductivity at temperatures as high as 250 K, have further stimulated an intense search for room-temperature superconductors in hydrides. This review focuses on the recent advances of crystal structures, stabilities, and superconductivity of lanthanide polyhydrides at high pressures, including the experimental results from our group. By using in situ four-probe electrical measurements and the synchrotron X-ray diffraction technique, we have identified several high-temperature superconducting phases: a lanthanum superhydride and two cerium superhydrides. The present work indicates that superconductivity declines along the La–Ce–Pr–Nd series, while magnetism becomes more and more pronounced. These discoveries have enriched the binary system of clathrate superhydrides and provided more hints for studying the role of rare earth metal elements having high-temperature superconductivity.

Introduction

Since Kamerlingh Onnes first discovered superconductivity with T_c∼4.2 K in mercury (Onnes, 1911), room-temperature superconductivity has been one of the most challenging projects in multiple fields such as physics and material science. In 1957, Bardeen, Cooper, and Schrieffer established the microscopic BCS theory to provide an explanation for conventional superconductors (Bardeen et al., 1957), which was also considered a road map to high-temperature superconductors. For these years, the search for superconducting materials with higher T_c has been ongoing. The famous and representative conventional superconductor MgB₂ had a T_c of 39 K at ambient pressure (Nagamatsu et al., 2001), which was far lower than the T_c for cuprates with 133 K (Iqbal et al., 1994). By the application of hydrostatic pressure, T_c of the HgBaCaCuO compound was increased to ∼164 K (Gao et al., 1994). However, cuprate-based superconductors are beyond the conventional BCS theory, and there is shortage of a generally accepted theory to explain the microscopic mechanism of them.

Back in 1935, Winger and Huntington proposed that hydrogen could be metallized under high pressure (Winger et al., 1935). According to the BCS theory, high phonon frequencies, large electronic density of states (DOS) near the Fermi level, and strong electron phonon coupling (EPC) can result in high T_c. In 1968, Ashcroft predicted that the realization of solid metallic hydrogen would open the pathway to high T_c superconductors (Ashcroft., 1968). Achieving a metallic state of hydrogen, referred to as metallic hydrogen, is dubbed as the Holy Grail in the high-pressure community. Experimental evidences on the transformation of hydrogen to the atomic state were reported close to 500 GPa (Loubeyre et al., 2020; Dias et al., 2017; Eremets et al., 2019), but such higher pressure limited its properties and application research. In 2004, Ashcroft suggested an alternative approach that metallization and superconductivity of hydrogen-rich compounds existed at much lower pressures (Ashcroft., 2004). Only 10 years later, Ashcroft’s idea found its experimental proofs, and extraordinarily, high-temperature superconductivities were demonstrated in compressed H₃S and LaH₁₀ (Drozdov et al., 2015; Einaga et al., 2016; Troyan et al., 2016; Huang et al., 2019; Somayazulu et al., 2019; Drozdov et al., 2019). It has been found that binary hydride LaH₁₀ can achieve high temperature superconductivity of 250–260 K, representing a new breakthrough in the binary system until now. These encouraging results have spurred a flurry of interests in other compressed hydrides, particularly for the ones from the same group. In this review, we are going to summarize the recent progresses on the lanthanide polyhydrides under high pressure. Through the discussions, we hope that some hints could be concluded for future studies in new hydrides with high-temperature superconductivity.

Dicussions

Lanthanum Superhydride

Lanthanum superhydride LaH₁₀ was first theoretically reported as a good candidate for high-T_c superconductivity (Peng et al., 2017; Liu et al., 2017), before experiments confirmed its high-temperature superconductivity (Somayazulu et al., 2019). Peng et al. and Liu et al. have independently performed systematic density functional theory (DFT) studies and proposed that the high-temperature superconducting phase fcc-LaH₁₀ with T_c reaching 280 K. fcc-LaH₁₀ showed a clathrate-like structure constituted by H cages, with La atoms occupying the fcc lattice positions. The high T_c has been explained as the strong electron -phonon coupling, which is associated with the strongly hybridized La f and H s orbitals (Liu et al., 2019; Wang et al., 2020). These theoretical predictions that lanthanum superhydride has great potential to be a near room-temperature superconductor have motivated experimental verifications. However, such experiments are very challenging, limited by hydrogen permeability and sample size.

Several experimental groups have successfully synthesized the predicted fcc-LaH₁₀ phase by laser heating La metal with pure hydrogen or ammonia borane (NH₃BH₃) at high pressure in a diamond anvil cell. The initial experimental observation of LaH_x with T_c at 215 K and 150 GPa was claimed by Drozdov et al. (Drozdov et al., 2018). They have obtained the target sample by heating the sample of La and pure hydrogen below 1,000 K at 170 GPa. The sample had a T_c of 209 K at 170 GPa, which increased to 215 K when the pressure reduced to 150 GPa. Then, Somayazulu et al. reported the superconducting lanthanum superhydride with T_c ∼ 260 K at 180–200 GPa (Somayazulu et al., 2019). Different from Drozdov et al., they chose ammonia borane as the hydrogen source. In addition, they also found that T_c decreased with increasing measuring current. Subsequently, Drozdov et al. changed the synthesized conditions and reported that LaH₁₀ had a highest T_c of 250 K at 170 GPa and decreased linearly as pressure increased (Drozdov et al., 2019). In their work, they also confirmed the crystal structure of LaH₁₀ as Fm $\overline{3}$ m symmetry via synchrotron X-ray diffraction and observed the isotope effects in the experiment. Besides those two groups, Hong et al. observed that the highest T_c for the La–H system was 246 K at 136 GPa (Hong et al., 2020), but the real phase was not known. Recently, Sun et al. found that T_c decreased to 191 K as the pressure dropped from 138 to 120 GPa, which was associated with the phase transition changing from Fm $\overline{3}$ m to C2/m (Sun et al., 2021).

During this time, we have also explored the superconductivity in the lanthanum superhydride. We used NH₃BH₃ as the hydrogen source considering the heating decompression reaction: NH₃BH₃→3H₂+c-BN (Chen et al., 2021; Shao et al., 2021b; Kondrat’ev et al., 2015). The La and NH₃BH₃ samples were loaded inside the hole of the gasket. We have applied the four-probe method to study the electrical resistance, and four Mo electrodes were sputtered onto the diamonds with a top flat of 60 μm beveled 300 μm, which have been successfully used in our previous work (Chen et al., 2021). The Raman shift of diamond was measured to calibrate the pressure (Akahama et al., 2006). By laser heating a mixture of La and NH₃BH₃ to about 1,400 K at 171 GPa, a resistance drop was triggered at about 238.4 K during the cooling cycle (Figure 1A). To further confirm this superconductivity, we have also measured the temperature-dependent electrical resistance under a series of applied magnetic fields from 0–6 T. T_c decreased along with the increasing magnetic fields, and the superconducting state was suppressed by the external magnetic fields, further proving the superconductivity. The upper critical magnetic fields were extrapolated based on the single-band Werthamer–Helfand–Hohenberg (WHH) (Werthamer et al., 1966) and Ginzburg–Landau (GL) (Ginzburg et al., 1950) models. The two models yielded the H_c2(0) as 158.1 and 114.9 T, respectively. These values are consistent with the reported experimental data (Drozdov et al., 2019). The coherence length can be calculated based on ${\mu }_0{H}_{c2}={\mathrm{\Phi }}_0/\left(2\pi {\xi }^2\right)$. The $\xi$ _WHH(0) and $\xi$ _GL (0) are equal to 1.44 and 1.69 nm, respectively. In Shukor’s work (Shukor, 2021), the value of coherence length for LaH₁₀ is 15.6–18.6 Å calculated by using $\xi$ _GL = 0.74 $\xi$ ₀ (1-T/T_c)^1/2, which is consistent with our work.

FIGURE 1

FIGURE 1. Our work measured the superconductivity of lanthanum superhydride at 171 GPa. (A) Temperature-dependent electrical resistance at 171 GPa during the cooling process and upon the external magnetic fields (0–6 T), measured by the four-probe technique. The inset shows that the sample chamber consists of La and NH₃BH₃ after laser heating. (B) Upper critical magnetic fields estimated by the single-band Werthamer–Helfand–Hohenberg (WHH) (Werthamer et al., 1966) and Ginzburg–Landau (GL) (Ginzburg et al., 1950) models.

Cerium Polyhydrides

From 2018, our group has carried out a series of work on cerium polyhydrides, particularly the discovery of two high-temperature superconducting cerium polyhydrides. Several new hydrides are studied by the treatment of different compression pathways (Li X. et al., 2019; Li et al., 2021). We have successfully synthesized a series of cerium polyhydrides by the direct reaction of Ce and H₂ upon cold compression up to 159 GPa (Li X. et al., 2019). The Ce polyhydrides (CeH₃, CeH_3+x, CeH₄, CeH_9-δ, and CeH₉) presented an increase of hydrogen content as pressure increased. The formed CeH₉ had a unique clathrate-like structure consisting of H29 cages surrounding Ce atoms occupying the hexagonal P6₃/mmc symmetry (see Figure 2A). CeH₉ was also with the nearest-neighbor H–H distances closest to predictions for solid atomic metallic hydrogen in all synthesized hydrides. The electron localization function of CeH₉ indicated an ionic bonding between Ce and H atoms, and the band structure confirmed its metallic character. The density of electronic-state calculations indicated the significant contribution of H at the Fermi level. Our cold-compression experiment provides a facile route to potential superconductors in superhydrides. The discovery of CeH₉ with atomic-like hydrogen sub-lattice suggests a low-pressure route for bulk dense atomic hydrogen stabilized by other element atoms. Independently, Salke et al. synthesized the clathrate hydride CeH₉ at 80–100 GPa by laser heating the mixture of the Ce sample and H₂ gas up to 2,000 K (Salke et al., 2019). They decompressed the sample and observed that the hexagonal CeH₉ became unstable below 93 GPa.

FIGURE 2

FIGURE 2. Crystal structures and superconducting transitions in the Ce–H system (Chen et al., 2021). (A) Crystal structures and hydrogen sub-lattice of P6₃/mmc-CeH₉ and Fm $\overline{3}$ m-CeH₁₀ phases. (B) Superconducting transitions for the Fm $\overline{3}$ m-CeH₁₀ phase determined by the electrical resistance measurements, with the external magnetic fields of 0–4 T at 95 GPa.

Recently, we have also further conducted deep experiments to explore the possible superconducting phases, and two phases were acquired: P6₃/mmc-CeH₉ and Fm $\overline{3}$ m-CeH₁₀ (Chen et al., 2021). The synchrotron X-ray diffraction verified that the superconductivity arose from CeH₉ and CeH₁₀. Both P6₃/mmc-CeH₉ and Fm $\overline{3}$ m-CeH₁₀ had high symmetric sodalite-like clathrate structures. For these two phases, zero resistance was evidenced by four-probe measurement in our experiment, which showed an obvious decrease of sample resistance during the cooling process. We first synthesized the Fm $\overline{3}$ m-CeH₁₀ phase, isostructural to Fm $\overline{3}$ m-LaH₁₀, which showed an almost linear increase of T_c during the release of pressure. The measured T_c reached 115 K at a pressure below 1 Mbar, as shown in (Figure 2B). In addition, the measured T_c also decreased with the enhancement of applied external magnetic fields.

The isotope effects were also experimentally observed by substituting the hydrogen in CeH₉ with heavier deuterium and the decreased T_c was measured, which substantiated the conventional electron–phonon coupling mechanism of the BCS theory. According to the reported theoretical calculations (Li B. et al., 2019; Peng et al., 2017), the much heavier and larger cerium atoms provided sufficient electrons to hydrogen and stabilized the H29 and H32 fascinating cages. The predicted E_f and electron–phonon coupling coefficient λ were both at high level, which contributed to an optimistic superconducting T_c. Presently, our result enriches the binary system of clathrate superhydrides and provides more evidence for studying the role of rare earth metal elements. This work also verifies that Ce is a potential choice for designing ternary or even more complex high-temperature superconducting hydrides.

Praseodymium and Neodymium Polyhydrides

We also performed a similar experimental method on the praseodymium and neodymium polyhydrides (Zhou et al., 2020a; Zhou et al., 2020b). Under high-pressure and high-temperature conditions, the introduction of lanthanide heavy metal atoms stabilized the hydrogen structure, and new superhydrides with high hydrogen content were obtained. We have adopted NH₃BH₃ as the hydrogen source, which greatly improved the success rate of experimental studies on superhydrides. At 130 GPa, we synthesized two novel superhydrides F $\overline{4}$ 3m-PrH₉ and P6₃/mmc-PrH₉, both of which had similar hydrogen-cage configurations as fcc-LaH₁₀ and P6₃/mmc-CeH₉. Resistance measurements showed that the synthesized mixture of cubic and hexagonal PrH₉ demonstrated a resistance drop around 9 K in high pressure, indicating a possible superconducting transition below 9 K (Zhou et al., 2020). Similar experimental methods were used in the Nd–H system, and three compounds, I4/mmm-NdH₄, C2/c-NdH_7, and P6₃/mmc-NdH_9, were obtained (Zhou et al., 2020b). The resistance measurements of synthesized NdH₉ demonstrated that there was no superconducting transition at 5–300 K over 100 GPa. Further calculation results showed that a magnetic order and electron–phonon interaction co-existed in a very close pressure range in praseodymium hydrides, which might have affected the low T_c. Subsequently, another group successfully synthesized several praseodymium polyhydrides at around 100 GPa (Pena-Alvarez et al., 2019). They heated the sample between 1,000 and 1,400 K at 85 GPa for 10 s, and both hexagonal PrH₇ and PrH₉ diffraction peaks could be observed in X-ray diffraction patterns. During the decompressing cycle, PrH₉ remained stable down to around 80 GPa, and the PrH₇ could decompose to PrH₄ below 54 GPa.

Our group has obtained new hydrides PrH₉ and NdH₉ in experiment. The theoretical calculations found that PrH₉ possessed weak superconductivity, while NdH₉ displayed strong magnetism (Zhou et al., 2020a; Zhou et al., 2020b). With the increase of f electrons, the outer f electrons had a significant effect on the superconductivity of these new superhydrides. The present results on lanthanide superhydrides show that superconductivity declines along the La–Ce–Pr–Nd series, while magnetism becomes more and more pronounced (see Figure 3). Generally, based on the BCS theory, the electron–phonon coupling directly affected the superconductivity of the conventional superconductors. The existence of magnetism prevented the formations of cooper pairs and then was not favorable to the superconductivity. Therefore, compared with lanthanum hydride, the increased number of f electrons in neodymium displayed pronounced magnetic properties, at the same time suppressing the conventional superconductivity based on electron–phonon coupling. It was further clarified that magnetism is an important factor to affect the conventional superconductivity in superhydrides.

FIGURE 3

FIGURE 3. Crystal structure and superconducting transition temperature T_c of novel lanthanide metal hydrides synthesized experimentally. (A) Crystal structures and hydrogen cage configurations of CeH₉, PrH_9, and NdH₉ found in this work; (B) Relationship of maximum T_c and outer f electrons of these new superhydrides.

Europium Polyhydrides

Europium as an active metal is a divalent element in general and reacts with hydrogen under pressure. Our previous work has obtained a series of Eu hydrides (F $\overline{4}$ 3m-EuH₉, P6₃/mmc-EuH₉ and Pm $\overline{3}$ n-Eu₈H₄₆) by laser heating the Eu metal and NH₃BH₃ at high pressure (Semenok et al., 2021). EuH₉ adopted F $\overline{4}$ 3m structure from 86 to 130 GPa, and the P6₃/mmc phase required higher stable pressure. We also discovered the Pm $\overline{3}$ n-Eu₈H₄₆ phase when heated to 1,600 K at 74 GPa, and the content of Eu₈H₄₆ increased as pressure increased. These three polyhydrides were all clathrate-like structures and magnetic. The Monte Carlo simulation suggested the anti-ferromagnetic ordering critical temperature for F $\overline{4}$ 3m-EuH₉ with T_N = 24 K. The P6₃/mmc-EuH₉ and Pm $\overline{3}$ n-Eu₈H₄₆ were calculated to be with ferromagnetic ordering critical temperatures T_c = 137 and 336 K, respectively. Ma et al. also obtained the same hexagonal clathrate-structure EuH₉ by laser heating samples to 2,800 K at 170 GPa (Ma et al., 2021). Moreover, they also obtained clathrate-structure EuH₆. Their electrical resistance measurements indicated the possible magnetic order transition temperature at 225 and 258 K for Pm $\overline{3}$ n-EuH₅ and Im $\overline{3}$ m-EuH₆, respectively. The weak superconductivity of Eu hydrides was attributed to the strong magnetism similar to Nd hydrides.

Other Heavy Lanthanide Polyhydrides

The heavy lanthanide hydrides are predicted as promising superconductors under pressure. Several groups have carried on the theoretical predictions of heavy lanthanide hydrides with high hydrogen content (Peng et al., 2017; Sun et al., 2020; Hai et al., 2021; Song et al., 2021). Peng et al. reported a serious of stable rare earth (RE) hydrides REH₆, REH₉, and REH₁₀ with unusual H clathrate structures at high pressure. The H-rich RE hydrides usually exhibited high-temperature superconductivity related to the H clathrate structures with strong EPC and large H-derived DOS near the Fermi surface, but the heavy lanthanide polyhydrides had much lower T_c due to heavier atoms which reduced the superconductivity (Peng et al., 2017). Subsequently, Sun et al. performed the EPC calculations for lanthanide hydrides with high hydrogen content and summarized the T_c for them. For the RE elements with half-filled 4f states (Eu, Gd, Dy, and Ho), they had the lowest DOS H-s values, resulting in a weak EPC and low T_c below 10 K. As the number of outer electrons increased, the T_cs for YbH₁₀ and LuH₈ reached as high as 102 K at 250 GPa and 86 K at 300 GPa, respectively (Sun et al., 2020). A series of stable superconducting Tb hydrides under pressure have been studied by Hai et al. TbH_n (n = 1, 2, 3) were predicted to be stable under low pressure, while the terbium hydrides with high hydrogen content were stable at high pressure. The terbium polyhydrides exhibited high-temperature superconductivity especially for Fm $\overline{3}$ m-TbH_10, with a T_c beyond 270 K above 230 GPa (Hai et al., 2021). The other theoretical work indicated that YbH₆ and LuH₆ showed the T_c as high as 145 K at 70 GPa and 273 K at 100 GPa, respectively (Song et al., 2021). In terms of the experiment, our work has successfully synthesized Fm $\overline{3}$ m-LuH₃ under high pressure (Shao et al., 2021a). The T_c for LuH₃ increased, first with compression to 15 K at 128 GPa, then decreased sharply, and increased to 14 K at 156 GPa at last. The upper critical magnetic fields H_c2(0) were estimated to be 8.47 and 7.17 T by WHH and GL models, respectively. The failure of synthesizing high T_c lutetium superhydrides above a pressure of 1 Mbar indicated that it was much tougher for Lu to form high hydrogen content hydrides than light lanthanide elements.

Perspective

It is important to find the high-temperature superconductors; at the same time, it is essential that the pressures required are reduced. Merit index S reflects the relationship between T_c and pressure (Pickard et al., 2020). We set S(MgB₂) as 1. A superconductor with a higher value of S means it has a higher critical temperature at mild pressure. As Figure 4 shows, LaH₁₀ and CeH₁₀ have high S values 1.35 and 1.12, which indicates that these hydrides have a stronger superconductivity under similar pressure. Thus, lanthanide elements have played a key role in forming high-temperature superconductors.

FIGURE 4

FIGURE 4. S for different superconducting hydrides reported from the experiment. Merit index S, can be explained as follows: S=T_c/(T²_c,MgB2+P²)^1/2 (Pickard et al., 2020; Shipley et al., 2021; Wang et al., 2021), where the temperature is expressed in Kelvin and the pressure is expressed in GPa. T_c,MgB2 is the superconductivity critical temperature of MgB₂ at ambient pressures, which equals to 39 K.

In conclusion, we summarize the experimental results of lanthanide hydrides at high pressure. The lanthanide hydrides with high hydrogen content have clathrate structures with hydrogen cages surrounding metal atoms and show cubic or hexagonal symmetries in general. Although several high-temperature superconducting lanthanum hydrides have been discovered, the extremely high synthetic pressures limit their practical applications. Therefore, there is still a long way to obtain a high-temperature superconductor at ambient pressure.

Author Contributions

XH conceived this project. SC and WC performed the experiment. JG analyzed the experimental data. XH and JG wrote and revised the article. All authors discussed the results and offered the useful discussions.

Funding

This work was supported by the National Key R&D Program of China (Grant No. 2018YFA0305900), the National Natural Science Foundation of China (Grant Nos. 11974133, 52072188, 51632002, and 51720105007), and the Program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT_15R23).

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s Note

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