Abstract
Inspired by the diverse properties of sulfur hydrides and phosphorus hydrides, we combine firstprinciples calculations with structure prediction to search for stable structures of Li−P−H ternary compounds at high pressures with the aim of finding novel superconductors. It is found that phosphorus hydrides can be stabilized under pressure via additional doped lithium. Four stable stoichiometries LiPH_{3}, LiPH_{4}, LiPH_{6}, and LiPH_{7} are uncovered in the pressure range of 100–300 GPa. Notably, we find an atomic LiPH_{6} with \(Pm\overline 3\) symmetry which is predicted to be a potential hightemperature superconductor with a T_{c} value of 150–167 K at 200 GPa and the T_{c} decreases upon compression. All the predicted stable ternary hydrides contain the P–H covalent frameworks with ionic lithium staying beside, but not for \(Pm\overline 3\)LiPH_{6}. We proposed a possible synthesis route for ternary lithium phosphorus hydrides: LiP + H_{2} → LiPH_{n}, which could provide helpful and clear guidance to further experimental studies. Our work may provide some advice on further investigations on ternary superconductive hydrides at high pressure.
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Introduction
Given the metallization and potential room temperature superconductivity of solid hydrogen under high pressure have been proposed,^{1,2} considerable efforts have been exerted in finding metallic hydrogen. Recently, solid hydrogen metallization has been reported to be realized at 495 GPa,^{3} but further evidence is needed. Although experimental observations of the metallic hydrogen phase remain controversial, researchers have agreed that hydrogen requires considerable high pressure to reach the metallic state. Doping hydrogen by an impurity has been considered a method for reducing the metallization pressure of pure hydrogen. Ashcroft^{4} suggested that the metallic hydrogenrich compounds, such as Group IVa dense hydrides, can be metallic at lower pressures than those necessary for hydrogen given the “precompression” provided by nonhydrogen elements. Extensive theoretical investigations have explored that many hydrogenrich compounds are potential superconductors with rather high superconducting transition temperature (T_{c}),^{5,6} such as H_{3}S with T_{c} of 204 K at 200 GPa,^{7,8} TeH_{4} with T_{c} of 104 K at 170 GPa,^{9} Si_{2}H_{6} with T_{c} of 139 K at 275 GPa,^{10} CaH_{6} of 235 K at 150 GPa,^{11} YH_{10} of 326 K at 250 GPa,^{12,13} LaH_{10} of 286 K at 210 GPa.^{12,13} Excitingly, hydrogenrich superconductors H_{3}S^{14,15} and LaH_{10}^{16,17} have been successfully confirmed experimentally.
Motivated by the discovery of the high T_{c} superconductor H_{3}S under high pressure, Eremets et al.^{18} compressed PH_{3} and found a T_{c} of 103 K at 207 GPa. However, the structural information and the origin of the high T_{c} phase were undetermined. Then, people have exerted efforts on determining this high T_{c} phase. Theoretical studies showed that all the predicted phosphorus hydrides PH_{n} (n = 1–6) at high pressure were thermodynamically metastable relative to elemental P and solid H_{2}.^{19,20,21} Among these metastable phases, PH_{2} possesses the lowest enthalpy with T_{c} of 76 K^{21} which responds to the superconducting phase in experimental work.^{18} Liu et al.^{20} theoretically searched the structure of PH_{3} under high pressure and found that the C2/m phase with T_{c} of 83 K at 200 GPa is in line with the experimental report.^{20} Experimentally, the PH_{3} is found to be gradually decomposed into P_{2}H_{4}, P_{4}H_{6}, and then further into elemental phases above 35 GPa at room temperature.^{22,23} But at lower temperature, P_{4}H_{6} can be stable up to 207 GPa.^{23}
Although phosphorus is adjacent to sulfur in the periodic table, and the predicted phosphorus hydrides have similar covalent bonds with those in sulfur hydrides, phosphorus hydrides are metastable, whereas sulfur hydrides prefer to form stable H_{3}S under high pressures. Considering that sulfur (3s^{2}3p^{4}) has one more valence electron than phosphorus (3s^{2}3p^{3}), phosphorus hydrides can be stabilized under pressure by introducing additional electrons. Therefore, we try to dope lithium into the P–H system, and expect to find the stable hydrogenrich ternary compounds with potential hightemperature superconductivity.
At present, researches on binary hydrogenrich superconducting compounds have been fruitful and matured, and ternary hydrogenrich superconducting compounds have gradually been taken seriously. Highpressure experiments found that the ternary hydride BaReH_{9} is a superconductor with T_{c} about 7 K at 100 GPa.^{24} Also in theoretical work, the T_{c} of Fe_{2}SH_{3},^{25} YS_{4}H_{4},^{26} and YSH_{5}^{27} at 173, 200, and 300 GPa is about 0.3, 20, and 0.7 K, respectively. Earlier, through theoretical calculations, our group found that after the introduction of Mg in the insulating CH_{4} system, the T_{c} of MgCH_{4} can reach 120 K at 121 GPa.^{28} Recently, K was also doped into the CH_{4} system in theoretical work^{29} and T_{c} was predicted to be 12.7 K at 80 GPa. In addtion, through adding Li into poor superconductive MgH_{12}, Sun et al.^{30} found a highT_{c} superconductor Li_{2}MgH_{16} with T_{c} about 473 K at 250 GPa. What is more, theoretical calculations show that the introduction of alkali metal and alkaline earth metal elements can make the binary Au–H system stable under ambient pressure, and T_{c} of the Ba(AuH_{2})_{2} under ambient pressure is approximate to be 30 K.^{31}
In fact, the precise exploration of the thermodynamic stability of the ternary stoichiometry system is a challenge. For the Li–P–H system, Li and P elements, Li–P, P–H, and Li–H binary boundary compounds are all systematically investigated and exhibit interesting superconducting properties under high pressure.^{18,19,20,21,22,23,32,33,34,35,36} Li–P compounds are well known as potential solidstate electrolytes in lithiumion batteries and recently was discovered to be superconductive in Li_{6}P with T_{c} about 39.3 K under high pressure.^{36} But LiP stoichiometry gets little attention owing to its poor Li content. At ambient condition, LiP is found to be stable and nonmetal with P2_{1}/c symmetry.^{37,38} Under high pressure,^{35,36} LiP firstly decomposes into Li_{3}P and P above 13.5 GPa, then it becomes stable again with P4/mmm symmetry above 60 GPa and retains stable till 300 GPa.
Here, we investigated the stabilities and structures of LiPH_{n} (n = 1–7) in the pressure range from 100 to 300 GPa through synthetic route LiP + H_{2} → LiPH_{n}. Hydrogenrich compositions, namely, LiPH_{3}, LiPH_{4}, LiPH_{6}, and LiPH_{7}, are found to be stable at high pressure. Above 250 GPa, LiPH_{6} is thermodynamically stable with \(Pm\overline 3\) symmetry, which is isostructural with ternary hydrides MgSiH_{6} and MgGeH_{6}.^{39,40} \(Pm\overline 3\)LiPH_{6} is calculated to be a potential highT_{c} superconductor with T_{c} about 150–167 K at 200 GPa and the T_{c} reduces with pressure increasing.
Results and discussion
We performed the full structure search of the Li–P–H ternary compounds at 100, 200, and 300 GPa by the ab initio evolutionary algorithm as implemented in the USPEX^{41,42} and constructed the ternary phase diagram in Fig. 1. It is shown that stoichiometries LiPH_{6} and LiPH_{7} locate on the convex hull at 100 and 200 GPa. Besides, we found two metastable compounds LiPH_{3} and LiPH_{4} which are only 9.9 and 2.0 meV/atom above the convex hull at 200 GPa. At 300 GPa, all ternary compounds become metastable, but LiPH_{6} and LiPH_{7} are only 9.1 and 7.0 meV/atom away from the convex hull, respectively. As expected, the LiPH_{n} compounds can be thermodynamically stable under high pressures. For judging the specific synthesis routes for ternary hydrides, our group proposed “triangle straightline method” (TSLM).^{31} Through this method, if one ternary compound in the ternary convex hull lies on a straight line connected by any two stable species, then the ternary compound can be synthesized by the two species. In the convex hull of Li–P–H, we found that the stable compounds LiPH_{6} and LiPH_{7} lie on the connecting straight line between LiP binary compounds and H_{2}. Herein, the synthetic route LiP + H_{2} → LiPH_{n} we have chosen for the lithium phosphorus ternary hydrides can be considered feasibly.
Furthermore, we conducted the structure predictions of LiPH_{n} (n = 1–7) with simulation size ranging from two to four for each stoichiometry at the 100, 200, 250, and 300 GPa. The energetic stabilities of LiPH_{n} (n = 1–7) compounds are evaluated by their formation enthalpies compared with LiP and H_{2}, as depicted in Fig. 2a. The stable structures of H_{2} were taken from the work of Pickard et al.,^{43} and LiP was taken from the work of Zhao et al.^{36} As observed, compared with LiP and H_{2} solids, the stoichiometries of LiPH, LiPH_{6}, and LiPH_{7} are stable and remain on the convex hull in the pressure range from 100 to 300 GPa; LiPH_{3} and LiPH_{4} emerge on the convex hull at 200 and 150 GPa and remain stable until 300 and 250 GPa, correspondingly. To further ensure the stabilities of ternary hydrides, we calculated the formation enthalpies of the abovementioned LiPH_{n} compounds with respect to two other routes (see Supplementary Fig. 1): Li_{3}P + P + H_{2} and LiH + P + H_{2}. With respect to Li_{3}P, P, and H_{2}, all the predicted phases are stable in the whole pressure range. With respect to LiH, P, and H_{2}, the LiPH becomes unstable in the whole pressure range. Combining the data given in the convex hull (Fig. 2a), the final phase diagram of LiPH_{n} is demonstrated in Fig. 2b. The LiPH_{3} is stable with P2/m structure from 200 to 300 GPa, and LiPH_{4} is stable with P2_{1}/m structure from 150 to 250 GPa. LiPH_{6} is stable with C2/c structure from 100 to 250 GPa and then convert into the cubic \(Pm\overline 3\) structure. LiPH_{7} started to be stable from 100 GPa with \(P\overline 1\) structure and transformed to C2/m structure at 250 GPa.
Zeropoint energy (ZPE) has been important in the total energy of hydrogenrich compounds. Therefore, we used the quasiharmonic model to estimate the ZPE of LiPH_{n} (n = 1–7) compounds under 300 GPa (see Supplementary Fig. 2). After considering the ZPE, the formation enthalpies of the predicted phases at 300 GPa are not various obviously and the overall stability does not change. Thus, the ZPE does not considerably influence the total stability of the phase diagram. The phonon band structures of all thermodynamically stable phases are exhibited in Supplementary Fig. 3. The lack of imaginary phonon frequency indicates that they are all dynamically stable.
A survey of the distinctive features of the predicted structures is displayed in Fig. 3, and the structure parameters are listed in Supplementary Table 1. For P2/mLiPH_{3} at 200 GPa, the P atoms formed distorted cubic units with the P–P bonds at approximately 2.10 Å. In the electron localization function (ELF) presented in Supplementary Fig. 4, electrons accumulate between P atoms, thereby indicating the P–P covalent bonds. The distorted cubic connected each other into a sheet with hydrogen saturating the dangling bonds. In the P–H sheets, every distorted cubic unit contains a monoatomic H at the center. Symmetrical with the P–H sheet, two other kinds of sheets are stacked along the baxis: one consists of Li atoms; another consists of H_{2} units with 0.88 Å bond lengths and monoatomic hydrogen atoms. For P2_{1}/mLiPH_{4} at 150 GPa, high electron densities are found between P–P and P–H in the ELF. Therefore, P atoms connect as zigzag chains with P–P bonds at approximately 2.10 Å. Every P atom connects four H atoms with P–H bonds ranging from 1.40 to 1.44 Å. Li atoms arrange along the P–H chains. When hydrogen content increases, as indicated in the ELF, P atoms absorb additional hydrogen atoms and form PH_{n} units. In C2/cLiPH_{6} and \(P\overline 1\)LiPH_{7} at 250 and 150 GPa, the PH_{6} units are found as distorted octahedrons with P–H bonds at approximately 1.35–1.36 and 1.37–1.40 Å, correspondingly. In the highpressure range, C2/mLiPH_{7} possesses PH_{11} units with P–H bonds at approximately 1.50–1.58 Å at 300 GPa. Every PH_{11} unit is connected by H–H bonds with 0.96 and 1.07 Å. At above 250 GPa, the C2/c phase of LiPH_{6} transforms into an A15like structure with \(Pm\overline 3\) symmetry, that is, isostructural with MgSiH_{6} and MgGeH_{6} predicted by our group.^{31,40} In \(Pm\overline 3\)LiPH_{6}, the H–H distances are 1.14 Å at 300 GPa and low electron densities between all the atoms in the ELF indicate the atomic character of this phase.
In previous theoretical works on the metastable P–H system, most PH_{n} (n = 1–3) structures consist of P–P layers or P–P chains with H atoms hanging on the P frameworks by P–H bonds.^{19,20,21} The dimensionality of the P frameworks decreases from layers (PH, PH_{2}) to chains (PH_{3}, PH_{4}). Then, in PH_{5} and PH_{6}, the P–H polymers exist and connected by H–H bonds.^{19} In LiPH_{n} (n = 1–7), except for the atomic phase \(Pm\overline 3\)LiPH_{6}, the P–H and P–P sublattices in LiPH_{n} (n = 1–7) structures are similar to those in the PH_{n} structures, that is, the layers of PH in LiPH_{3}, the chains of PH_{4} in LiPH_{4}, and the polymers of PH_{6} and PH_{11} in LiPH_{6} and LiPH_{7}. Thus, lithium does not change the connect manner of phosphorus and hydrogen but stabilize the phosphorus hydrides under high pressure.
Before calculating the superconductive properties of LiPH_{n} compounds, we explored their electronic structures. In the calculated band structures with projection (Fig. 4), except for the lowpressure phases C2/mLiPH_{6} and \(P\overline 1\)LiPH_{7}, all the other stable phases are metallic. The bands near the Fermi level are mainly provided by H and P and rarely come from Li. The Bader charge analysis^{44} (see Supplementary Table 6) shows that Li and P atoms play roles as electron donors and provide electrons to H atoms. For all the stable phases, Li constantly loses approximately 0.8e. This phenomenon indicates that, for every metastable PH_{n}, nearly one electron is required for their stabilization, and this requirement is satisfied by lithium. However, the electrons that P loses and the electrons that H gains are different from each stable phase. For nonmetallic phase C2/cLiPH_{6} and \(P\overline 1\)LiPH_{7}, and poor metallic phase P2_{1}/mLiPH_{4}, every P atom loses approximately 2.88, 2.76, and 1.43e, and every H atom receives nearly 0.61, 0.51, and 0.56e, respectively. For other metallic phases P2/mLiPH_{3}, \(Pm\overline 3\)LiPH_{6}, and C2/mLiPH_{7}, every P atom loses 0.23, 1.28, and 1.23e and every H atom receives 0.33, 0.34, and 0.29e, correspondingly. In metallic phases, fewer electrons around H atoms than those in nonmetallic and poor metallic phases are present, thereby indicating more free electrons in metallic phases. With the increase in the H contents in metallic phases, the Hderived electronic DOS gradually dominates at the Fermi level N_{F} (Fig. 5). For P2/mLiPH_{3}, the values Pderived electronic DOS contribute most to the N_{F}. For \(Pm\overline 3\)LiPH_{6} and C2/mLiPH_{7}, the values of N_{F} are mainly contributed by electrons projected to the H atoms. Therefore, the hydrogenrich LiPH_{n} compounds may produce promising superconductivities.
We investigated the superconductivities of the metallic LiPH_{n} compounds at different pressures by calculating the EPC parameter λ, the logarithmic average phonon frequency ω_{log}, and the superconductive critical temperature T_{c} (Table 1). For poor metallic phase P2_{1}/mLiPH_{4} at 150 GPa, the λ is 0.25, and ω_{log} is 1222.8 K. The small values of λ and ω_{log} cause the low T_{c} at approximately 0.05 K, which is close to 0. For P2/mLiPH_{3} and C2/mLiPH_{7}, the EPC parameters of λ are 0.82 and 0.74, and the calculated ω_{log} values are 1131.5 and 1434.0 K at 200 and 300 GPa, respectively. Using the corrected Allen–Dynesmodified McMillan equation, their T_{c} values are 48.8–60.4 and 46.0–59.2 K with the Coulomb pseudopotential μ* = 0.1–0.13, correspondingly.
Although atomic phase \(Pm\overline 3\)LiPH_{6} starts to be stable above 250 GPa, we found that it can be dynamically stable when decompressed to 200 GPa, and we calculated the superconducting critical temperature T_{c} of \(Pm\overline 3\)LiPH_{6} as a function of pressure (Table 1). At 200, 250, and 300 GPa, the calculated values of T_{c} are 167.3, 148.3, and 128.6 K, respectively. The Eliashberg phonon spectral function α^{2}F(ω) and projected phonon density of states (PHDOS) of \(Pm\overline 3\)LiPH_{6} at different pressures are illustrated in Fig. 6. Under the pressures of 200, 250, and 300 GPa, the contributions of Li, P, and H atoms to the total λ and total ω_{log} are shown in Fig. 6. The P atoms dominate the lowfrequency regions (0–500 cm^{−1}) which contribute about 23.0–31.7% to the total λ and 5.7–8.6% to the total ω_{log}. For the case of Li atoms, they dominate the middlefrequency regions (500–1000 cm^{−1}), contribute about 13.0–17.8% to the total λ, and 3.8–3.9% to the total ω_{log}. While the H atoms which dominate the highfrequency regions (>1000 cm^{−1}) contribute about 55.3–59.2% to the total λ and 87.5–90.4% to the total ω_{log}. Hydorgen plays a dominating role in electron–phonon coupling and logarithmic average phonon frequency. Therefore, the high T_{c} of \(Pm\overline 3\)LiPH_{6} mainly comes from H atoms.
With the increase in pressure, the T_{c} decreases from 167.7 to 128.6 K. At the same time, the ω_{log} increases from 1119.2 to 1429.4 K whereas λ decreases from 1.62 to 1.11. Therefore, the change of T_{c} is dominated by λ under pressure. We further studied the change of the partial ω_{log} and λ of Li, P, and H atoms under pressure (Table 2). From 200 to 300 GPa, the ω_{logP} reduces from 96.1 to 81.4 K while the ω_{logLi} increases from 43.8 to 55.6 K. As a result, the total value of low and middlefrequency ω_{logLiP} are almost unchanged under pressure. The increase of ω_{log} is mainly due to the increase of ω_{logH} (from 979.3 to 1292.4 K). With the increase of pressure, the partial constants of EPC λ_{H} and λ_{P} reduce a lot from 0.895 to 0.675 and 0.515 to 0.256, respectively, while the λ_{Li} varies little from 0.210 to 0.197. Thus, the decrease of λ is mainly dominated by the reduction of λ_{H} and λ_{P}, which is due to the large contribution of H and P atoms to the Fermi level N_{F}.
The predicted metastable superconductor PH_{3} possesses T_{c} at approximately 83 K with estimated λ and ω_{log} at nearly 1.45 and 826 K for 200 GPa.^{20} At the same pressure, \(Pm\overline 3\)LiPH_{6} has a T_{c} at approximately 149.6–167.3 K with λ and ω_{log} at nearly 1.62 and 1119.2 K, respectively. The λ and ω_{log} values of \(Pm\overline 3\)LiPH_{6} are larger than those of PH_{3}, thus causing a larger T_{c}. The doping of Li atom makes the total mass of LiPH_{6} lighter than that of PH_{3}, which can produce a large Debye temperature. Moreover, three clear phonon frequency regions that correspond to P, Li, and H can be found in \(Pm\overline 3\)LiPH_{6} and the atomic H has a wide and continuous highvibration frequency region (1000–2500 cm^{−1}) and contributes considerably to the EPC. In the case of PH_{3}, strong hybridization of P and H makes the low and middlefrequency regions contribute most to the total EPC, thereby possibly causing a low λ value.
To further explore the superconductivities and provide some information to experiment, the McMillan isotopic coefficient β and critical magnetic fields μ_{0}H_{c}(0) of LiPH_{n} (n = 3, 6, and 7) and critical temperature T_{c} of LiPD_{n} (n = 3, 6, and 7) are estimated in Table 1. Because the T_{c} of LiPH_{4} is near zero, we did not calculate its β, μ_{0}H_{c}(0), and T_{c} of LiPD_{4}. It is clear that the isotopic coefficient β values always maintain about 0.5. For P2/mLiPH_{3} and C2/mLiPH_{7}, the critical magnetic fields μ_{0}H_{c}(0) are estimated to be about 6.8–8.5 and 6.4–8.4 T at 200 and 300 GPa, respectively. For the highT_{c} superconductor \(Pm\overline 3\)LiPH_{6}, the estimated μ_{0}H_{c}(0) value is as high as 28.7–32.9 T at 200 GPa, and gradually decreases to 16.1–19.0 T at 300 GPa.
In summary, we have explored the crystal structures and stabilities of Li−P−H ternary system under high pressure by employing the evolutionary algorithm USPEX in combination with firstprinciples calculations. It is found that Li can stabilize metastable P–H compounds and form stable ternary hydrides LiPH_{3}, LiPH_{4}, LiPH_{6}, and LiPH_{7} under high pressure. Except for the lowpressure phases of C2/cLiPH_{6} and \(P\overline 1\)LiPH_{7}, all the other stable LiPH_{n} phases are metallic. Among the metallic phases, P2/mLiPH_{3} and C2/mLiPH_{7} are superconductive with T_{c} of 49–60 and 46–59 K at 200 and 300 GPa, respectively. Their critical magnetic fields are about 6–8 T. Significantly, atomic phase \(Pm\overline 3\)LiPH_{6} has a high T_{c} and high μ_{0}H_{c}(0) values about 149–167 K and 28.7–32.9 T at 200 GPa, respectively. As pressure increases to 300 GPa, the T_{c} and μ_{0}H_{c}(0) decrease to 110–128 K and 16.1–19.0 T, correspondingly. The high T_{c} value of \(Pm\overline 3\)LiPH_{6} under pressure is closely related to the large Hderived electronic DOSs at the Fermi level, strong EPC and high logarithmic average frequency associated with vibrations of atomic H, and the light masses of Li atoms. The exploration of ternary phase diagrams is a challenging task, but the study of ternary hydrides remains valuable. Ternary hydrides frequently achieve some goals that are unachievable in binary hydrides by introducing a third type of element, such as stabilizing the metastable binary hydrides, metalizing the insulative binary hydrides with strong covalent bonds, further reducing the superconducting pressures of some high T_{c} binary hydrides. Furthermore, ternary hydrides may produce some other new high T_{c} phases, such as the atomic phase of \(Pm\overline 3\)LiPH_{6}.
Methods
Variable composition searches of the Li–P–H ternary phase at 100, 200, and 300 GPa were conducted through the evolutionary algorithm USPEX^{41,42} code with respect to element Li, P, and H. One hundred and twenty structures were created using a random symmetric generator in the first generation, all subsequent generations contained 85 structures and were produced using variation operators such as heredity (50%), softmutation (20%), transmutation (10%), 20% of each new generation was produced randomly. Then, we explored the stable compounds of LiPH_{n} (n = 1–7) based on the fixed composition search implemented by USPEX^{41,42} with respect to the binary compounds LiP and H_{2}. It was performed at 100, 200, 250, and 300 GPa using original cells ranging from two to four formula units. All the structural relaxations, electronic properties, and total energy calculations are conducted using the VASP package^{45} in the framework of DFT with Perdew–Burke–Ernzerhof parameterization of the generalized gradient approximation.^{46} The projectoraugmented wave approach^{47} was adopted to describe ion–electron interactions, where 1s^{1}, 1s^{2}2s^{1}, and 3s^{2}3p^{3} are considered as valence electrons for H, Li, and P atoms, respectively. A planewave energy cutoff of 800 eV was used. We applied a Brillouin zone sampling grid spacing of 2π × 0.03Å^{−1} for structure relaxations and 2π × 0.02Å^{−1} for electronic property calculations. Lattice dynamics and electron–phonon coupling (EPC) were characterized by density functional perturbation theory as implemented in the QuantumESPRESSO package.^{48} Normconserving potentials for H (1s^{1}), Li (1s^{2}2s^{1}), and P (3s^{2}3p^{3}) were used with a kinetic energy cutoff of 80 Ry. The k and qpoints meshes in the first BZ are 24 × 12 × 24 and 4 × 2 × 4 for P2/mLiPH_{3}, 20 × 20 × 12 and 5 × 5 × 3 for P2_{1}/mLiPH_{4}, 24 × 24 × 24 and 6 × 6 × 6 for \(Pm\overline 3\)LiPH_{6}, and 20 × 20 × 12 and 5 × 5 × 3 for C2/cLiPH_{7}. Their superconductive transition temperatures T_{c} are estimated through the Allen−Dynesmodified McMillan equation with correction factors.^{49} The calculation details of superconductive properties can be seen in Supplementary Information.
Data Availability
The datasets used in this article are available from the corresponding author upon request.
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Acknowledgements
This work was supported by the National Key R&D Program of China (No. 2018YFA0305900), National Natural Science Foundation of China (Nos. 51632002, 11674122, 51572108, 11634004, 11504127, 11574109, 11704143, 11404134), Program for Changjiang Scholars and Innovative Research Team in University (No. IRT_15R23), the 111 Project (No. B12011). Parts of calculations were performed in the High Performance Computing Center (HPCC) of Jilin University and TianHe1(A) at the National Supercomputer Center in Tianjin.
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T.C. and D.D. designed this projected. Z.S. performed the calculations. D.D. and Z.S. made the analysis and wrote the manuscript. All authors discussed the results and commented on the manuscript.
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Shao, Z., Duan, D., Ma, Y. et al. Ternary superconducting cophosphorus hydrides stabilized via lithium. npj Comput Mater 5, 104 (2019). https://doi.org/10.1038/s4152401902446
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DOI: https://doi.org/10.1038/s4152401902446
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