Superconducting phase diagram of H3S under high magnetic fields

Superior Superconducting Properties Realized in Quaternary La-Y-Ce Hydrides at Moderate Pressures

The recent revolution in the superconductivity field stems from hydride superconductors. Multicomponent hydrides provide a crucial platform for tracking high-temperature superconductors. Besides high superconducting transition temperature (Tc), achieving both giant upper critical magnetic field [μ0Hc2(0)] and high critical current density [Jc(0)] is also key to the latent potential of the application for hydride superconductors. In this work, we have successfully synthesized quaternary La-Y-Ce hydrides with excellent properties under moderate pressure by using the concept of "entropy engineering." The obtained temperature dependence of the resistance provides evidence for the superconductivity of Fm3m-(La,Y,Ce)H10, with the maximum Tc ∼ 190 K (at 112 GPa). Notably, Fm3m-(La,Y,Ce)H10 boasts exceptional properties: μ0Hc2(0) reaching 292 T and Jc(0) surpassing 4.61 × 107 A/cm2. Compared with the binary LaH10/YH10, we find that the Fm3m structure in (La,Y,Ce)H10 can be stable at relatively low pressures (112 GPa). These results indicate that multicomponent hydrides can significantly enhance the superconducting properties and regulate stabilizing pressure through the application of "entropy engineering." This work stimulates the experimental exploration of multihydride superconductors and also provides a reference for the search of room-temperature superconductors in more diversified hydride materials in the future.

High-temperature superconductivity up to 223 K in the Al stabilized metastable hexagonal lanthanum superhydride

As compressed hydrides constantly refresh the records of superconducting critical temperatures (Tc) in the vicinity of room temperature, this further reinforces the confidence to find more high-temperature superconducting hydrides. In this process, metastable phases of superhydrides offer enough possibilities to access superior superconducting properties. Here we report a metastable hexagonal lanthanum superhydride (P63/mmc-LaH10) stabilized at 146 GPa by introducing an appropriate proportion of Al, which exhibits high-temperature superconductivity with Tc ∼ 178 K, and this value is enhanced to a maximum Tc ∼ 223 K at 164 GPa. A huge upper critical magnetic field value Hc2(0) reaches 223 T at 146 GPa. The small volume expansion of P63/mmc-(La, Al) H10 compared with the binary LaH10 indicates the possible interstitial sites of Al atoms filling into the La-H lattice, instead of forming conventional ternary alloy-based superhydrides. This work provides a new strategy for metastable high-temperature superconductors through the multiple-element system.

The effect of critical coupling constants on superconductivity enhancement

In this study, we propose a phenomenological model to extend McMillan's results on a coupling strength equal to 2. We investigate possible strategies to enhance superconductivity by tuning the phonon frequency, carrier number, or pressure. In particular, we show that the critical coupling constants corresponding to the phonon frequency, carrier number, or pressure determine whether the variation of the critical temperature is positive or negative. These observations explain the contrasting behavior between weak and strong coupling superconductors and are consistent with experimental observations. We also demonstrate the dome observed in the carrier number effect and pressure effect. Additionally, these critical coupling constants systematically separate superconductivity into three regions: weak, intermediate, and strong coupling. We find that the enhancement strategies for weak and strong coupling regions are opposite, but both inevitably bring superconductivity into the intermediate coupling region. Finally, we propose general zigzag methods for intermediate coupling superconductors to further enhance the critical temperature.

D-Wave Superconducting Gap Symmetry as a Model for Nb1−xMoxB2 (x = 0.25; 1.0) and WB2 Diborides

Recently, Pei et al. (National Science Review2023, nwad034, 10.1093/nsr/nwad034) reported that ambient pressure β-MoB2 (space group: R3¯m) exhibits a phase transition to α-MoB2 (space group: P6/mmm) at pressure P~70 GPa, which is a high-temperature superconductor exhibiting Tc=32 K at P~110 GPa. Although α-MoB2 has the same crystalline structure as ambient-pressure MgB2 and the superconducting critical temperatures of α-MoB2 and MgB2 are very close, the first-principles calculations show that in α-MoB2, the states near the Fermi level, εF, are dominated by the d-electrons of Mo atoms, while in MgB2, the p-orbitals of boron atomic sheets dominantly contribute to the states near the εF. Recently, Hire et al. (Phys. Rev. B2022, 106, 174515) reported that the P6/mmm-phase can be stabilized at ambient pressure in Nb1−xMoxB2 solid solutions, and that these ternary alloys exhibit Tc~8 K. Additionally, Pei et al. (Sci. China-Phys. Mech. Astron. 2022, 65, 287412) showed that compressed WB2 exhibited Tc~15 K at P~121 GPa. Here, we aimed to reveal primary differences/similarities in superconducting state in MgB2 and in its recently discovered diboride counterparts, Nb1−xMoxB2 and highly-compressed WB2. By analyzing experimental data reported for P6/mmm-phases of Nb1−xMoxB2 (x = 0.25; 1.0) and highly compressed WB2, we showed that these three phases exhibit d-wave superconductivity. We deduced 2Δm(0)kBTc=4.1±0.2 for α-MoB2, 2Δm(0)kBTc=5.3±0.1 for Nb0.75Mo0.25B2, and 2Δm(0)kBTc=4.9±0.2 for WB2. We also found that Nb0.75Mo0.25B2 exhibited high strength of nonadiabaticity, which was quantified by the ratio of TθTF=3.5, whereas MgB2, α-MoB2, and WB2 exhibited TθTF~0.3, which is similar to the TθTF in pnictides, A15 alloys, Heusler alloys, Laves phase compounds, cuprates, and highly compressed hydrides.

Quantifying Nonadiabaticity in Major Families of Superconductors

The classical Bardeen−Cooper−Schrieffer and Eliashberg theories of the electron−phonon-mediated superconductivity are based on the Migdal theorem, which is an assumption that the energy of charge carriers, kBTF, significantly exceeds the phononic energy, ℏωD, of the crystalline lattice. This assumption, which is also known as adiabatic approximation, implies that the superconductor exhibits fast charge carriers and slow phonons. This picture is valid for pure metals and metallic alloys because these superconductors exhibit ℏωDkBTF<0.01. However, for n-type-doped semiconducting SrTiO3, this adiabatic approximation is not valid, because this material exhibits ℏωDkBTF≅50. There is a growing number of newly discovered superconductors which are also beyond the adiabatic approximation. Here, leaving aside pure theoretical aspects of nonadiabatic superconductors, we classified major classes of superconductors (including, elements, A-15 and Heusler alloys, Laves phases, intermetallics, noncentrosymmetric compounds, cuprates, pnictides, highly-compressed hydrides, and two-dimensional superconductors) by the strength of nonadiabaticity (which we defined by the ratio of the Debye temperature to the Fermi temperature, TθTF). We found that the majority of analyzed superconductors fall into the 0.025≤TθTF≤0.4 band. Based on the analysis, we proposed the classification scheme for the strength of nonadiabatic effects in superconductors and discussed how this classification is linked with other known empirical taxonomies in superconductivity.

Effect of Magnetic Impurities on Superconductivity in LaH10

Polyhydrides are a novel class of superconducting materials with extremely high critical parameters, which is very promising for sensor applications. On the other hand, a complete experimental study of the best so far known superconductor, lanthanum superhydride LaH₁₀ , encounters a serious complication because of the large upper critical magnetic field H_C2 (0), exceeding 120-160 T. It is found that partial replacement of La atoms by magnetic Nd atoms results in significant suppression of superconductivity in LaH₁₀ : each at% of Nd causes a decrease in T_C by 10-11 K, helping to control the critical parameters of this compound. Strong pulsed magnetic fields up to 68 T are used to study the Hall effect, magnetoresistance, and the magnetic phase diagram of ternary metal polyhydrides for the first time. Surprisingly, (La,Nd)H₁₀ demonstrates completely linear H_C2 (T) ∝ |T - T_C |, which calls into question the applicability of the Werthamer-Helfand-Hohenberg model for polyhydrides. The suppression of superconductivity in LaH₁₀ by magnetic Nd atoms and the robustness of T_C with respect to nonmagnetic impurities (e.g., Y, Al, C) under Anderson's theorem gives new experimental evidence of the isotropic (s-wave) character of conventional electron-phonon pairing in lanthanum decahydride.

Magnetic field screening in hydrogen-rich high-temperature superconductors

In the last few years, the superconducting transition temperature, Tc, of hydrogen-rich compounds has increased dramatically, and is now approaching room temperature. However, the pressures at which these materials are stable exceed one million atmospheres and limit the number of available experimental studies. Superconductivity in hydrides has been primarily explored by electrical transport measurements, whereas magnetic properties, one of the most important characteristic of a superconductor, have not been satisfactory defined. Here, we develop SQUID magnetometry under extreme high-pressure conditions and report characteristic superconducting parameters for Im-3m-H3S and Fm-3m-LaH10-the representative members of two families of high-temperature superconducting hydrides. We determine a lower critical field Hc1 of ∼0.82 T and ∼0.55 T, and a London penetration depth λL of ∼20 nm and ∼30 nm in H3S and LaH10, respectively. The small values of λL indicate a high superfluid density in both hydrides. These compounds have the values of the Ginzburg-Landau parameter κ ∼12-20 and belong to the group of "moderate" type II superconductors, rather than being hard superconductors as would be intuitively expected from their high Tcs.

High-Temperature Superconducting Phase in Clathrate Calcium Hydride CaH_{6} up to 215 K at a Pressure of 172 GPa

The recent discovery of superconductive rare earth and actinide superhydrides has ushered in a new era of superconductivity research at high pressures. This distinct type of clathrate metal hydrides was first proposed for alkaline-earth-metal hydride CaH_{6} that, however, has long eluded experimental synthesis, impeding an understanding of pertinent physics. Here, we report successful synthesis of CaH_{6} and its measured superconducting critical temperature T_{c} of 215 K at 172 GPa, which is evidenced by a sharp drop of resistivity to zero and a characteristic decrease of T_{c} under a magnetic field up to 9 T. An estimate based on the Werthamer-Helfand-Hohenberg model gives a giant zero-temperature upper critical magnetic field of 203 T. These remarkable benchmark superconducting properties place CaH_{6} among the most outstanding high-T_{c} superhydrides, marking it as the hitherto only clathrate metal hydride outside the family of rare earth and actinide hydrides. This exceptional case raises great prospects of expanding the extraordinary class of high-T_{c} superhydrides to a broader variety of compounds that possess more diverse material features and physics characteristics.

High-temperature superconductivity on the verge of a structural instability in lanthanum superhydride

The possibility of high, room-temperature superconductivity was predicted for metallic hydrogen in the 1960s. However, metallization and superconductivity of hydrogen are yet to be unambiguously demonstrated and may require pressures as high as 5 million atmospheres. Rare earth based “superhydrides”, such as LaH₁₀, can be considered as a close approximation of metallic hydrogen even though they form at moderately lower pressures. In superhydrides the predominance of H-H metallic bonds and high superconducting transition temperatures bear the hallmarks of metallic hydrogen. Still, experimental studies revealing the key factors controlling their superconductivity are scarce. Here, we report the pressure and magnetic field dependence of the superconducting order observed in LaH₁₀. We determine that the high-symmetry high-temperature superconducting Fm-3m phase of LaH₁₀ can be stabilized at substantially lower pressures than previously thought. We find a remarkable correlation between superconductivity and a structural instability indicating that lattice vibrations, responsible for the monoclinic structural distortions in LaH₁₀, strongly affect the superconducting coupling.

The experimental studies to understand the superconductivity of superhydrides remain scarce. Here, the authors report pressure and magnetic field dependence of superconductivity in LaH₁₀, and indicate lattice vibrations strongly affect superconducting coupling.

Superconductivity up to 243 K in the yttrium-hydrogen system under high pressure

The discovery of superconducting H3S with a critical temperature Tc∼200 K opened a door to room temperature superconductivity and stimulated further extensive studies of hydrogen-rich compounds stabilized by high pressure. Here, we report a comprehensive study of the yttrium-hydrogen system with the highest predicted Tcs among binary compounds and discuss the contradictions between different theoretical calculations and experimental data. We synthesized yttrium hydrides with the compositions of YH3, YH4, YH6 and YH9 in a diamond anvil cell and studied their crystal structures, electrical and magnetic transport properties, and isotopic effects. We found superconductivity in the Im-3m YH6 and P63/mmc YH9 phases with maximal Tcs of ∼220 K at 183 GPa and ∼243 K at 201 GPa, respectively. Fm-3m YH10 with the highest predicted Tc > 300 K was not observed in our experiments, and instead, YH9 was found to be the hydrogen-richest yttrium hydride in the studied pressure and temperature range up to record 410 GPa and 2250 K.

Classifying Charge Carrier Interaction in Highly Compressed Elements and Silane

Since the pivotal experimental discovery of near-room-temperature superconductivity (NRTS) in highly compressed sulphur hydride by Drozdov et al. (Nature 2015, 525, 73-76), more than a dozen binary and ternary hydrogen-rich phases exhibiting superconducting transitions above 100 K have been discovered to date. There is a widely accepted theoretical point of view that the primary mechanism governing the emergence of superconductivity in hydrogen-rich phases is the electron-phonon pairing. However, the recent analysis of experimental temperature-dependent resistance, R(T), in H₃S, LaH_x, PrH₉ and BaH₁₂ (Talantsev, Supercond. Sci. Technol. 2021, 34, accepted) showed that these compounds exhibit the dominance of non-electron-phonon charge carrier interactions and, thus, it is unlikely that the electron-phonon pairing is the primary mechanism for the emergence of superconductivity in these materials. Here, we use the same approach to reveal the charge carrier interaction in highly compressed lithium, black phosphorous, sulfur, and silane. We found that all these superconductors exhibit the dominance of non-electron-phonon charge carrier interaction. This explains the failure to demonstrate the high-T_c values that are predicted for these materials by first-principles calculations which utilize the electron-phonon pairing as the mechanism for the emergence of their superconductivity. Our result implies that alternative pairing mechanisms (primarily the electron-electron retraction) should be tested within the first-principles calculations approach as possible mechanisms for the emergence of superconductivity in highly compressed lithium, black phosphorous, sulfur, and silane.

Comparison of highly-compressedC2/m-SnH12superhydride with conventional superconductors

Satterthwaite and Toepke (1970Phys. Rev. Lett.25741) predicted high-temperature superconductivity in hydrogen-rich metallic alloys, based on an idea that these compounds should exhibit high Debye frequency of the proton lattice, which boosts the superconducting transition temperature,T_c. The idea has got full confirmation more than four decades later when Drozdovet al(2015Nature52573) experimentally discovered near-room-temperature superconductivity in highly-compressed sulphur superhydride, H₃S. To date, more than a dozen of high-temperature hydrogen-rich superconducting phases in Ba-H, Pr-H, P-H, Pt-H, Ce-H, Th-H, S-H, Y-H, La-H, and (La, Y)-H systems have been synthesized and, recently, Honget al(2021arXiv:2101.02846) reported on the discovery ofC2/m-SnH₁₂phase with superconducting transition temperature ofT_c∼ 70 K. Here we analyse the magnetoresistance data,R(T,B), ofC2/m-SnH₁₂phase and report that this superhydride exhibits the ground state superconducting gap of Δ(0) = 9.2 ± 0.5 meV, the ratio of 2Δ(0)/k_BT_c= 3.3 ± 0.2, and 0.010 <T_c/T_F< 0.014 (whereT_Fis the Fermi temperature) and, thus,C2/m-SnH₁₂falls into unconventional superconductors band in the Uemura plot.

Quantifying the Charge Carrier Interaction in Metallic Twisted Bilayer Graphene Superlattices

The mechanism of charge carrier interaction in twisted bilayer graphene (TBG) remains an unresolved problem, where some researchers proposed the dominance of the electron-phonon interaction, while the others showed evidence for electron-electron or electron-magnon interactions. Here we propose to resolve this problem by generalizing the Bloch-Grüneisen equation and using it for the analysis of the temperature dependent resistivity in TBG. It is a well-established theoretical result that the Bloch-Grüneisen equation power-law exponent, p, exhibits exact integer values for certain mechanisms. For instance, p = 5 implies the electron-phonon interaction, p = 3 is associated with the electron-magnon interaction and p = 2 applies to the electron-electron interaction. Here we interpret the linear temperature-dependent resistance, widely observed in TBG, as p→1, which implies the quasielastic charge interaction with acoustic phonons. Thus, we fitted TBG resistance curves to the Bloch-Grüneisen equation, where we propose that p is a free-fitting parameter. We found that TBGs have a smoothly varied p-value (ranging from 1.4 to 4.4) depending on the Moiré superlattice constant, λ, or the charge carrier concentration, n. This implies that different mechanisms of the charge carrier interaction in TBG superlattices smoothly transition from one mechanism to another depending on, at least, λ and n. The proposed generalized Bloch-Grüneisen equation is applicable to a wide range of disciplines, including superconductivity and geology.

Synthesis of Yttrium Superhydride Superconductor with a Transition Temperature up to 262 K by Catalytic Hydrogenation at High Pressures

The recent observation of room-temperature superconductivity will undoubtedly lead to a surge in the discovery of new, dense, hydrogen-rich materials. The rare earth metal superhydrides are predicted to have very high-T_{c} superconductivity that is tunable with changes in stoichiometry or doping. Here we report the synthesis of an yttrium superhydride that exhibits superconductivity at a critical temperature of 262 K at 182±8  GPa. A palladium thin film assists the synthesis by protecting the sputtered yttrium from oxidation and promoting subsequent hydrogenation. Phonon-mediated superconductivity is established by the observation of zero resistance, an isotope effect and the reduction of T_{c} under an external magnetic field. The upper critical magnetic field is 103 T at zero temperature.

Composite pressure cell for pulsed magnets

Extreme pressures and high magnetic fields can affect materials in profound and fascinating ways. However, large pressures and fields are often mutually incompatible; the rapidly changing fields provided by pulsed magnets induce eddy currents in the metallic components used in conventional pressure cells, causing serious heating, forces, and vibration. Here, we report a diamond-anvil-cell made mainly out of insulating composites that minimizes inductive heating while retaining sufficient strength to apply pressures of up to 8 GPa. Any residual metallic component is made of low-conductivity metals and patterned to reduce eddy currents. The simple design enables rapid sample or pressure changes, desired by pulsed-magnetic-field-facility users. The pressure cell has been used in pulsed magnetic fields of up to 65 T with no noticeable heating at cryogenic temperatures. Several measurement techniques are possible inside the cell at temperatures as low as 500 mK.

A Boosted Critical Temperature of 166 K in Superconducting D3 S Synthesized from Elemental Sulfur and Hydrogen

The discovery of superconductivity in H3 S at 203 K marked an advance towards room-temperature superconductivity and demonstrated the potential of H-dominated compounds to possess a high critical temperature (Tc ). 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 Tc was determined correctly for samples prepared from compressed H2 S, since they are inevitably contaminated with H-depleted byproducts. Here, we prepare stoichiometric H3 S by direct in situ synthesis from elemental S and excess H2 . The Im 3 ‾ m phase of D3 S samples exhibits a Tc significantly higher than previously reported values (ca. 150 K), reaching a maximum Tc of 166 K at 157 GPa. Furthermore, we confirm that the sharp decrease in Tc 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.

Origin of enhanced chemical precompression in cerium hydride [Formula: see text]

The rare-earth metal hydrides with clathrate structures have been highly attractive because of their promising high-[Formula: see text] superconductivity at high pressure. Recently, cerium hydride [Formula: see text] composed of Ce-encapsulated clathrate H cages was synthesized at much lower pressures of 80-100 GPa, compared to other experimentally synthesized rare-earth hydrides such as [Formula: see text] and [Formula: see text]. Based on density-functional theory calculations, we find that the Ce 5p semicore and 4f/5d valence states strongly hybridize with the H 1s state, while a transfer of electrons occurs from Ce to H atoms. Further, we reveal that the delocalized nature of Ce 4f electrons plays an important role in the chemical precompression of clathrate H cages. Our findings not only suggest that the bonding nature between the Ce atoms and H cages is characterized as a mixture of ionic and covalent, but also have important implications for understanding the origin of enhanced chemical precompression that results in the lower pressures required for the synthesis of [Formula: see text].

Classifying Induced Superconductivity in Atomically Thin Dirac-Cone Materials

Recently, Kayyalha et al. (Phys. Rev. Lett., 2019, 122, 047003) reported on the anomalous enhancement of the self-field critical currents (Ic (sf, T)) at low temperatures in Nb/BiSbTeSe2-nanoribbon/Nb Josephson junctions. The enhancement was attributed to the low-energy Andreev-bound states arising from the winding of the electronic wave function around the circumference of the topological insulator BiSbTeSe2 nanoribbon. It should be noted that identical enhancement in Ic (sf, T) and in the upper critical field (Bc2 (T)) in approximately the same reduced temperatures, were reported by several research groups in atomically thin junctions based on a variety of Dirac-cone materials (DCM) earlier. The analysis shows that in all these S/DCM/S systems, the enhancement is due to a new superconducting band opening. Taking into account that several intrinsic superconductors also exhibit the effect of new superconducting band(s) opening when sample thickness becomes thinner than the out-of-plane coherence length (c (0)), we reaffirm our previous proposal that there is a new phenomenon of additional superconducting band(s) opening in atomically thin films.