Abstract
High pressure structure, stability, metallization and superconductivity of PbH_{4}(H_{2})_{2}, a H_{2}containing compound combining one of the heaviest elements with the lightest element, are investigated by the firstprinciples calculations. The metallic character is found over the whole studied pressure range, although PbH_{4}(H_{2})_{2} is metastable and easily decompose at low pressure. The decomposition pressure point of 133 GPa is predicted above which PbH_{4}(H_{2})_{2} is stable both thermodynamically and dynamically with the C2/m symmetry. Interestedly, all hydrogen atoms pairwise couple into H_{2} quasimolecules and remain this style up to 400 GPa in the C2/m structure. At highpressure, PbH_{4}(H_{2})_{2} tends to form the PbH_{2} alloy. The superconductivity of T_{c} firstly rising and then falling is observed in the C2/m PbH_{4}(H_{2})_{2}. The maximum of T_{c} is about 107 K at 230 GPa. The softening of intermediatefrequency phonon induced by more inserted H_{2} molecules is the main origin of the high T_{c}. The results obtained represent a significant step toward the understanding of the high pressure behavior of metallic hydrogen and hydrogenrich materials, which is helpful for obtaining the higher T_{c}.
Introduction
In recent decades, many scientists have devote to searching for the hightemperature superconducting materials. For the lightest element, hydrogen (H), Ashcroft applied the BCS theory to propose that the metallic hydrogen will be a roomtemperature superconductor under high pressure^{1}. This suggestion has motivated considerable experimental and theoretical activities. However, solid hydrogen remains insulating character at extremely high pressure, at least up to 342 GPa^{2}. Due to the extremely high and experiment unreachable pressure, as a alternative, Ashcroft proposed that the hydrogenrich alloys shall transform into metal under relatively lower pressure due to the chemical precompressions from the comparable weight elements^{3}. Thus, hydrogenrich groupIV hydrides have been extensively explored, such as CH_{4}, SiH_{4}, GeH_{4}, SnH_{4} and PbH_{4}. All of them show up interesting new structures and novel properties under pressure. CH_{4} is still an insulator up to the pressure of 520 GPa^{4}. Although Eremets et al. experimentally reported the metallization and superconductivity of SiH_{4} above 60 GPa^{5}, for the controversial result it might be understood as superconductivity of amorphous silicon, silicon hydrides, or platinum hydrides^{6,7}. And theoretical prediction indicates that the stable SiH_{4} can behave as metal and exhibit superconductivity above 220 GPa with the superconducting transition temperature (T_{c}) of about 20 K (The Coulomb parameter , the below is same.)^{8}. GeH_{4} has lower metallization pressure than silane^{9,10} and the highest T_{c} reaches to 73 K at 220 GPa^{11}. Furthermore, the metallization pressure of SnH_{4} decreases, the highest T_{c} is close to 83 K at 120 GPa^{12}.
It is clearly that the metallization pressure of groupIV hydrides decreases with increase of atomic number of heavy element, which is obviously less than that of solid H_{2}. Unfortunately, the T_{c} of groupIV hydrides is also greatly decreased. By analyzing the crystal feature, we find that the quasimolecular H_{2} units exist in the highpressure structures of GeH_{4} and SnH_{4}. And these H_{2} units have been found to contribute significantly to the superconductivity. Then, whether can the T_{c} be improved by intercalating H_{2} into groupIV hydrides? H_{2}containing compounds of CH_{4}H_{2} have been fabricated up to 30 GPa, such as CH_{4}(H_{2})_{2}, (CH_{4})_{2}H_{2}, CH_{4}(H_{2})_{4}, CH_{4}H_{2}^{13}. But both metallization and superconductivity are still lack. For the SiH_{4}H_{2} system, the crystal structure, phase diagram and metallization under pressure of SiH_{4}(H_{2})_{2} were extensively explored^{14,15,16,17,18,19,20,21,22}. The T_{c} of SiH_{4}(H_{2})_{2} is as high as 107 K at 250 GPa^{23}, which is visibly higher than that of SiH_{4}. Following the experimental observation^{24}, we have also theoretically investigated the structural, phase transition, metallization and superconductivity of GeH_{4}(H_{2})_{2} under pressure^{25,26}. The predicted T_{c} of GeH_{4}(H_{2})_{2} is close to 100 K at 250 GPa, higher than that of GeH_{4}. These results inevitably encourage us further to seek for hightemperature superconductors and study the superconductivity in these H_{2}containing compounds. However, it is necessary to decrease the work pressure of superconducting. For examples, the decomposition pressures are as high as 248 GPa for SiH_{4}(H_{2})_{2} and 220 GPa for GeH_{4}(H_{2})_{2}, respectively, above which they are stable superconducting materials.
As mentioned above, the combination the lightest H with one of the heaviest Pb seems to be a good way to improve the T_{c} and decrease the work pressure. Chemically, PbH_{4} still remains the most elusive of groupIV tetrahydrides. The pioneering theoretical work of Desclaux and Pyykkö predicted the structure and stability of PbH_{4}^{27,28}. The theoretically predicted tetrahedral structure of an isolated molecule, with an equilibrium PbH distance of approximately 1.73 Å, was eventually confirmed by experiments^{29,30}. But, Krivtsun et al.^{30} observed that the PbH_{4} molecules were kinetically unstable and readily decompose to Pb atomic layer and H_{2} in approximately 10 s. Recently, ZaleskiEjgierd et al. theoretically investigated the structure and the stability of PbH_{4} under high pressure^{31}. They found that PbH_{4} is stable thermodynamically above 132 GPa, in forms of Imma (132–296 GPa) and Ibam (>296 GPa) space groups. And PbH_{4} even keeps the metallic character covering the whole range of pressure^{31}. However, the superconductivity is indeterminate, since the dynamic stable phase of PbH_{4} has been not discovered from experimental and theoretical aspects yet. By intercalating H_{2} units into PbH_{4} molecular crystal, e.g. PbH_{4}(H_{2})_{2}, how about the structure, stability and superconductivity? It is just the purpose of our study. In this work, we found out the stable phase of PbH_{4}(H_{2})_{2} thermodynamically and dynamically and investigated its desired superconductivity. The decomposition pressure of 133 GPa is much lower than the metallization pressure of solid hydrogen, which is easily reached in experiments by diamondanvil techniques. And the H_{2}H_{2} coupling under high pressure figures out the different superconducting mechanism.
Results
Covering the wide pressure range of 0–400 GPa, variablecell structure prediction simulations with 1 to 4 PbH_{4}(H_{2})_{2} formula units per cell (f.u./cell) were performed. We have calculated the enthalpies of searched structures of PbH_{4}(H_{2})_{2} to examine the thermodynamical stability induced by pressure. For several competitive structures of PbH_{4}(H_{2})_{2}, the enthalpies (relative to the P1 structure) as function of pressure are shown in Fig. 1. It is found that Pnnm phase is the most stablest below 40 GPa with the lowest enthalpy value. Starting from 40 GPa up to 135 GPa, PbH_{4}(H_{2})_{2} transfers into P1 phase. Upon further compression, the C2/m becomes to the most stablest phase above 135 GPa. As a result, there are two structural phase transitions existing in the range of 0–400 GPa. Three lowenthalpy structures were obtained, orthorhombic Pnnm (4 f.u./cell), triclinic P1 (2 f.u./cell) and monoclinic C2/m (2 f.u./cell), respectively, as shown in Supplementary Fig. S1 online. The lattice parameters of these three structures at different pressures are also listed in Table S1 of the supplementary information online. From the crystal configurations at different pressures, PbH_{4} tetrahedral molecule does not exist in PbH_{4}(H_{2})_{2} and all of hydrogen atoms construct the H_{2} quasimolecules separating from Pb atoms.
However, it was reported that the hydrogenrich materials is easily decomposed^{10,11,15,16,17,22,23,24,25,31,32}. Hence, we must check the stability by mean of estimating the decomposition enthalpy. For PbH_{4}(H_{2})_{2}, there are five possible decomposition paths as PbH_{4}(H_{2})_{2} → Pb + 4H_{2}, 2PbH_{4}(H_{2})_{2} → 2PbH + 7H_{2}, PbH_{4}(H_{2})_{2} → PbH_{2} + 3H_{2}, 2PbH_{4}(H_{2})_{2} → 2PbH_{3} + 5H_{2} and PbH_{4}(H_{2})_{2} → PbH_{4} + 2 H_{2}, respectively. For three system of PbH_{3}, PbH_{2} and PbH, we searched their structures at different pressures. Structural parameters at different pressure regions are presented in Supplementary (Tables S2, S3 and S4) online. With help of the reported structures of Pmnm, P6/mmm, Imma and Ibam for PbH_{4}^{31}, fcc, hcp and for Pb^{33}, P6_{3}m, C/2c and Cmca for H_{2}^{34} corresponding stable pressures, the decomposition enthalpies were calculated and plotted in Fig. 1. PbH_{4}(H_{2})_{2} is unstable and decomposes into Pb + 4H_{2} blow 120 GPa and PbH_{4} + 2H_{2} in the pressure range of 120–160 GPa. Namely, both Pnnm and P1 phases are metastable. PbH_{4}(H_{2})_{2} is only stabilized above the pressure of 160 GPa, displaying the symmetry of C2/m.
Besides, it has wellknown that quantum effects related to hydrogen atoms are very important. The hydrogen zeropoint energy (ZPE) has significantly revised the structural stability as in the cases of solid hydrogen^{34} and hydrogenrich materials^{9,11}. To judge the effect on stability, we also calculated the ZPEs of PbH_{4}(H_{2})_{2}, PbH_{4} and H_{2} in the range of 100–200 GPa using the quasiharmonic approximation^{35}. As the insert shown in Fig.1, the ZPE effect does not change the order of the phase transitions but lowers the decomposition pressure of the C2/m structure into ~133 GPa. This decomposition pressure of PbH_{4}(H_{2})_{2} is obviously lower than 248 GPa of SiH_{4}(H_{2})_{2}^{23} and 220 GPa of GeH_{4}(H_{2})_{2}^{25}, which indicates that PbH_{4}(H_{2})_{2} will exist in the wider pressure range. For this stability, the subsequent crystal structural, electronic, phonon and electronphonon coupling (EPC) calculations are focused on the C2/m structure above 133 GPa and typical results are presented at 200 GPa.
For C2/m structure, Pb atoms occupy the crystallographic 2a sites and four nonequivalent H atoms sit on the 4i sites under high pressure. All of H atoms pairwise coupling into two types of quasimolecules as shown in Fig. 2a. The nearest distance between Pb and H atom is about 2 Å. In this dense structure, we can not find any plumbane molecules existing, but H_{2} quasimolecules distribute around Pb atoms and are ordering (Fig. 2). This kind of ordered arrangements of H_{2} units is clearer at high pressure, while H_{2} units tend to be inordering at low pressure^{18,25}. A visible character of Pb and H_{2} in layers is observed from (001)plane (Fig. 2b) or (010)plane (Fig. 2c). Noticeably, the layered feature is also a common phenomenon in some hydrogenrich systems. With the increase of pressure, all of the lattice constants of C2/m structure in a, b and c directions decrease. However, the HH bond lengths in H_{2} quasimolecules marked as d1_{H−H} (formed by H1 and H2 sites shown in Fig. 2a) and d2_{H−H} (formed by H3 and H4 sites shown in Fig. 2a) firstly increase then decrease as shown in Fig. 3a. There are three kinds of intermolecular distances among H_{2} molecules in the C2/m structure, all of them are monotonously decreased with the pressurizing, as shown in Fig. 3b. Reviewing the highpressure structural character, we find that part hydrogen atoms form H_{2} units with the other hydrogen atoms strongly bonding with Si in Ccca phase of SiH_{4}(H_{2})_{2}^{23}, while all of hydrogen atoms pairwise coupling into H_{2} quasimolecules with the nearest distance of ~1.7 Å between Ge and H in P2_{1}/c phase of GeH_{4}(H_{2})_{2}^{25}. As a comparison, with the help of analysis of atomic distances, the intermolecular and intramolecular couplings of H_{2} gradually strengthen, while the interaction between H and the heavy atom evidently weakens from SiH_{4}(H_{2})_{2} to GeH_{4}(H_{2})_{2} and then to PbH_{4}(H_{2})_{2}.
At 200 GPa, the lattice parameters of C2/m structure are a = 7.184 Å, b = 2.807 Å and c = 2.973 Å, as well as the angle β = 68.1° (see Supplementary Table S1 online). The d1_{H−H} and d2_{H−H} are 0.78 Å and 0.82 Å, respectively. The intermolecular distance of H_{2}H_{2} is less than that between Pb and H atoms. With the lattice parameters, calculated electronic structures show that PbH_{4}(H_{2})_{2} is metallic at 200 GPa. For SiH_{4}(H_{2})_{2} and GeH_{4}(H_{2})_{2} reported previously, they remain the characteristics of insulator under low pressure. The insulatortometal transition occurs at 92 GPa in SiH_{4}(H_{2})_{2} and at 48 GPa in GeH_{4}(H_{2})_{2}, respectively. However, we didn’t find the transition point of PbH_{4}(H_{2})_{2}. It seems to be metal even in ambient pressure, which consist with PbH_{4}^{31}. So the low pressure metallization does not come from the intercalation of H_{2} molecules. Comparing with Si and Ge, Pb has larger ionic radius which results in more strong itinerant property of valent electrons. Figure 4 shows the projected density of state (PDOS) at several selected pressures. According to the electronic PDOS at Fermi level we can draw a conclusion that at low pressure in Pnnm structure the Pbp electrons make the most contribution to density of state and exhibit properties of a nearly freeelectron metal (Fig. 4a,b). As the pressure increases, the strengthening of H_{2}H_{2} interaction leads to the overlap of Hs wave functions. The contribution of Hs electrons to Fermi surface increases. PDOS tends to be uniform distribution and the bandwidth further broadens from 100 GPa to 300 GPa (Fig. 4c–f). It indicates that with the increase of pressure PbH_{4}(H_{2})_{2} mainly like to be PbH_{2} alloy. The Pb interlayer interaction is connected by these H_{2} molecules. To gain more insight into the bonding nature of PbH_{4}(H_{2})_{2}, the electron location function (ELF) of C2/m phase at 200 GPa was calculated. ELF shown in Fig. 5 displays the electronic location around Pb and H atoms as well as the nearly freeelectronlike distribution among Pb atoms. However, the high ELF values between Pb and H atoms (Fig. 5a) and of intermolecular H_{2} (Fig. 5b) indicate that the electrons become delocalized, suggesting a feature of nearly freeelectron metal.
The phonon dispersion curves for C2/m structure at 200 GPa (Fig. 6) and other selected pressure point (see Supplementary Fig. S2 online) were calculated to explore the lattice dynamics of PbH_{4}(H_{2})_{2}. The absence of any imaginary frequencies implies the dynamical stability of C2/m phase under high pressure. The whole phonon spectrum can be divided into three parts. By combining with the phonon density of states (PhDOS) projected on atoms shown in Fig. 7a, in the case of 200 GPa, we find that the lowfrequency vibration below 215 cm^{−1} mainly come from the vibrations Pb atoms. The intermolecular strong phonon coupling among H_{2} molecules appear in the intermediatefrequency range of 295–1876 cm^{−1}. After a large gap, in high frequency area above 2695 cm^{−1}, the HH vibration in H_{2} formed by H3 and H4 sites mainly contributes in the range of 2695–2898 cm^{−1}, while the vibration in H_{2} formed by H1 and H2 sites around 3220 to 3380 cm^{−1}. Comparing these three systems of Si, Ge and Pbbased, we find a strong phonon coupling between silicon and hydrogen in SiH_{4}(H_{2})_{2}^{23}, very weak phonon coupling between metal and hydrogen in GeH_{4}(H_{2})_{2}^{25} as well as PbH_{4}(H_{2})_{2}. The HH vibration in H_{2} molecule is the strongest in PbH_{4}(H_{2})_{2}. From the Eliashberg phonon spectral function α^{2}F(ω) and the integrated EPC parameter λ(ω) shown in Fig. 7b, the intermediatefrequency (295–1876 cm^{−1}) vibrational modes of H_{2} molecules contribute 81.5% of total λ. This percentage is larger than 66% in Sibased and 75% in Gebased case. This result highlights the significant role played by H_{2} molecules on the electronphonon interaction.
At 200 GPa, the calculated total EPC constant λ is 1.296 for C2/m PbH_{4}(H_{2})_{2}. From Si to Ge and then to Pb case, the λ gradually decreases from 1.625 to 1.43 and then to 1.296, which implies a weak coupling between metal and hydrogen. However, the phonon frequency logarithmic average ω_{log} rises gradually, from 871 K in SiH_{4}(H_{2})_{2} to 1051 K in PbH_{4}(H_{2})_{2}. This means more higher Debye temperature in PbH_{4}(H_{2})_{2}. Based on the obtained α^{2}F(ω) and λ(ω), we now can analyze the superconductivity using the modified McMillan equation by Allen and Dynes^{36},
With the typical choice of the Coulomb pseudopotential ^{3}, a remarkable large T_{c} of 103 K was obtained for C2/m phase of PbH_{4}(H_{2})_{2}, which is comparable with those of copper oxide superconductors.
To figure out the pressure effect on superconductivity in PbH_{4}(H_{2})_{2}, in addition, the T_{c} values at several typical pressure points were calculated and shown in Supplementary Fig. S3 online. An interesting phenomenon exhibits the superconductivity firstly strengthening before weakening. The T_{c} has a maximum between 140 and 350 GPa, ~107 K for . Seen from the distances of among H_{2} molecules shown in Fig. 3b, the monotonously decreasing makes a hint of “hardening” of intermediatefrequency phonon with the increase of pressure. The phonon spectra shown in Supplementary Fig. S2 online confirm this point. To analyze this phenomenon of T_{c} variations, we have further calculated the Eliashberg phonon spectral function and the EPC strength at different pressures, the results are presented in Supplementary Fig. S4 online. With the increase of pressure, the calculated EPCs are 1.280, 1.296, 1.379 and 1.341 for 180 GPa, 200 GPa, 250 GPa and 300 GPa, respectively, which shows a tendency of first increase and then decrease similar to T_{c}. In the T_{c} rising zone, the contribution of PbH coupling to the EPC strength is decreased from 14.3% at 180 GPa to 12% at 200 GPa and the phonon vibration of HH in H_{2} units also weakens the EPC (The contribution is from 7.3% to 6.5% corresponding pressures.). However, the contribution of H_{2}H_{2} coupling to the EPC is strengthening from 78.4% at 180 GPa to 81.5% at 200 GPa. So the initial rising of T_{c} results from the contribution increasing of H_{2}H_{2} for the EPC. As shown in Fig. S4 online, from 75.8% at 250 GPa to 73.5% at 300 GPa, the decrease of contribution of H_{2}H_{2} for the EPC leads to the fall of T_{c}. The result further reveals the significance of H_{2}H_{2} coupling to superconductivity in PbH_{4}(H_{2})_{2}.
Discussion
Thus far, the stability of PbH_{4}(H_{2})_{2} has been identified in the pressure range of 0–400 GPa. At low pressure it is metastable and possibly decomposes into Pb + H_{2} or PbH_{4} + H_{2}. Above 133 GPa, it is stable not only thermodynamically but also dynamically. This highpressure stable phase of C2/m exhibits the expected superconductivity of T_{c} ~ 107 K at 230 GPa, which is obviously higher than those of conventional groupIV hydrides such as silane, germane and stannane. Noticeably, the coupling between groupIV element and hydrogen reduces with the increase of atomic number. Namely, the contribution of groupIV element to total EPC decreases in hydrides from 33% in SiH_{4}(H_{2})_{2}^{23} to 25% in GeH_{4}(H_{2})_{2}^{25} and then to 12% in PbH_{4}(H_{2})_{2}. On the contrary, the coupling among H_{2} molecules strengthens as mentioned above. Particularly, we want to point out that the T_{c} (~100 K) is comparable for SiH_{4}(H_{2})_{2}, GeH_{4}(H_{2})_{2} and PbH_{4}(H_{2})_{2} at the same Coulomb pseudopotential, though the superconducting mechanism is incompletely same. The intercalating H_{2} molecules into groupIV hydrides really improves the T_{c}. From the phonon contribution to EPC, we find that the intermediatefrequency phonon is dominated. Comparing with corresponding SiH_{4}^{8}, GeH_{4}^{11} and SnH_{4}^{12}, it is clear that the intercalation of H_{2} molecules results in the softening of intermediatefrequency phonon. As increasing the content of hydrogen in groupIV elements, it results in enhancing the EPC strength that is dominated by the coupling of the H_{2} molecular in the AH_{4}(H_{2})_{2} (A = Si, Ge, Sn and Pb) crystals. This is just the origin of higher T_{c} in H_{2}containing compounds. Furthermore, we infer that the higher T_{c} may be obtained if more H_{2} are inserted in groupIV hydrides. Actually, more future works are needed to advance the T_{c} and understand the superconductivity.
As a comparison, the highpressure structure of PbH_{4}(H_{2})_{2} is visibly different from other hydrogenrich compounds with high T_{c}, such as CaH_{6}^{37} and (H_{2}S)_{2}H_{2}^{32}. In highpressure structures of CaH_{6} and (H_{2}S)_{2}H_{2}, the H_{2} quasimolecules have been broken, with the strong bonds forming between metal and hydrogen atoms. Although the EPC is mainly contributed by hydrogen, the superconducting mechanism is different. It is the HH coupling in CaH_{6} and (H_{2}S)_{2}H_{2}, while the H_{2}H_{2} coupling in PbH_{4}(H_{2})_{2}. It is interested that the H_{2} quasimolecule form keeps all along at thus high pressure up to 400 GPa. At the same time, Pb is one of the heaviest elements. The combination with the lightest H is one of the most important physical problems in highpressure research. Pb metal makes the metallization pressure of hydrogenrich compound decrease. Remarkably, the decomposition pressure point (133 GPa) of PbH_{4}(H_{2})_{2} is the lowest among these H_{2}containing compounds of Si, Ge and Pbbased. This value is much lower than the metallization pressure of bulk molecular hydrogen, which indicates the feasibility to experimentally observe. Hence, Pbbased hydrides are the potential candidates as highT_{c} superconductors. Our finding may hopefully stimulate the potential highT_{c} superconductors research in H_{2}containing hydrides.
Methods
The search for crystalline structures of PbH_{4}(H_{2})_{2} phases was performed using particle swarm optimization methodology as implemented in the CALYPSO program^{38,39}. Structural optimizations, enthalpies and electronic structures were calculated using the Vienna ab initio simulation (VASP) program^{40,41} and projectoraugmented plane wave (PAW) potentials employing the PerdewBurkeErnzerhof (PBE) functional^{42}. The 1s^{1} and 6s^{2}6p^{2} electrons were included in the valence space for H and Pb atoms, respectively. For the planewave basisset expansion, an energy cutoff of 800 eV was used. Dense kpoint meshes were employed to sample the first Brillouin zone (BZ) and ensured that energies converged to within 1 meV/atom. All forces acting on atoms were converged 0.001 eV/Å or less and the total stress tensor was reduced to the order of 0.01 GPa. With the noteworthy mass ratio 207:1 between Pb and H, we have involved the spinorbit effect in this calculation.
Based on the optimized structures from VASP, lattice dynamics and superconducting properties were calculated using density functional perturbation theory^{43} and the TroullierMartins normconserving potentials^{44}, as implemented in the QUANTUMESPRESSO code^{45}. The cutoff energies of 60 and 400 Ry were used for wave functions and charge densities, respectively. 12 × 12 × 8 MonkhorstPack kpoint grid with Gaussian smearing of 0.03 Ry was used for the phonon calculations at 3 × 3 × 2 qpoint mesh and double kpoint grid was used in the calculation of the electronphonon interaction matrix element.
Additional Information
How to cite this article: Cheng, Y. et al. Pressureinduced superconductivity in H_{2}containing hydride PbH_{4}(H_{2})_{2}. Sci. Rep. 5, 16475; doi: 10.1038/srep16475 (2015).
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Acknowledgements
The work was supported by the National Basic Research Program of China (973 Program) under Grant no. 2012CB933700, the Natural Science Foundation of China (Grant nos 11274335, 61274093, U1230202 and 91230203), the Shenzhen Basic Research Grant (Nos KQC201109050091A and JCYJ20120617151835515) and the Dong Guan foundation under Grant no. 2014509121212.
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G.H.Z. and C.L.Y. designed research. Y.C., C.Z. and T.T.W. performed research. Y.C., C.Z., T.T.W., C.L.Y., G.H.Z., X.J.C. and H.Q.L. analyzed the results. Y.C., C.L.Y. and G.H.Z. wrote the first draft of the paper and all authors contributed to revisions. All authors reviewed the manuscript.
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Cheng, Y., Zhang, C., Wang, T. et al. Pressureinduced superconductivity in H_{2}containing hydride PbH_{4}(H_{2})_{2}. Sci Rep 5, 16475 (2015). https://doi.org/10.1038/srep16475
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DOI: https://doi.org/10.1038/srep16475
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