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Prediction of Superconductivity in Clathrate Er Hydrides under High Pressure

School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China
School of Physics and Electronic Information, Gannan Normal University, Ganzhou 341000, China
Author to whom correspondence should be addressed.
Crystals 2023, 13(5), 792;
Submission received: 26 March 2023 / Revised: 29 April 2023 / Accepted: 3 May 2023 / Published: 9 May 2023
(This article belongs to the Section Inorganic Crystalline Materials)


In this paper, we perform unbiased structure searches combined with first-principles calculations to predict the stable structures and possible superconductivity of ErHn (n = 4~6) under pressures of 50~300 GPa. Two novel compounds, ErH4 and ErH6, are identified as thermodynamically and dynamically stable above 50 GPa; ErH4 and ErH6 can stabilize in clathrate structures with the I4/mmm and Im 3 ¯ m space groups, respectively. An analysis of the electronic density of states (DOS) suggests the metallic nature of the two phases. Then, the superconducting critical temperature (Tc) is estimated using the Allen–Dynes modified McMillan equation; the results are 130.9~181.2 K for Im 3 ¯ m-ErH6 at 100~300 GPa, and 74.4~79.8 K for I4/mmm-ErH4 at 150~300 GPa. The resultant high Tc superconductivity in this system can be traced back to the combination of high density of states at the Fermi level and strong electron–phonon interactions.

1. Introduction

Searching for high-temperature superconductors is a hot topic in condensed-matter physics and materials science [1,2,3,4,5,6]. Metallic hydrogen has been predicted to be a superconductor with high transition temperatures [1]. However, it is technically difficult to attain metallic states of hydrogen through static compression experiments. Searching for high-Tc superconductors has, in turn, transformed to some other systems such as hydrogen-dominant compounds [2]. According to Ashcroft’s prediction [2], hydrogen-rich hydrides can be metallized at much lower pressures compared to elemental hydrogen due to chemical “pre-compression” effects, and therefore, may be potential superconductors with high Tc. This finding promoted the subsequent upsurge in the study of hydrides and which has eventually led to the discovery of a plethora of superconducting hydrides.
Alkali metals (AM = Li, Na, K, Rb, and Cs) comprise one of the most reactive groups of elements that can react with hydrogen at atmospheric conditions, forming alkali hydrides in the rock–salt (B1) structure with AMH stoichiometry. These hydrides are classic ionic compounds with large energy band gaps of 4~6 eV [7]. Although theoretical calculations have suggested that pressure-induced metallization takes place at ~300 GP, these systems are not good candidates for high temperature superconductivity even under high pressures, since they are unlikely to have high density of states (DOS) values at the Fermi level (EF). However, by compressing mixtures of AMH and H2, alkali metal subhydrides (AMHx, x > 1) have been predicted to become stable (or metastable) under high pressures [8,9]. Among these alkali metal subhydrides, LiH6 (with R3m symmetry), LiH8 (with I422 symmetry), and KH6 (with C2/c symmetry) are superconductors with Tc values of 38~82 K at 150~300 GPa, 31~37 K at 100~200 GPa, and 46~70 K at 230~300 GPa, respectively [10,11]. These calculations suggest that alkali metal hydrides with high DOS values at EF are more likely to have high Tc superconductivity.
Meanwhile, alkaline earth metal hydrides have also been studied using DFT calculations [12,13]. Due to the lower DOS values at EF, BeH2 and MgH2 have been predicted to have smaller Tc values of 32~44 K at 250 GPa [12] and 16~23 K at 180 GPa [13], respectively. However, by increasing the H content, CaH6 [14] and MgH6 [15], calculations have shown they can be stable above 150 GPa. Interestingly, both of the hydrides crystalize in sodalite-like clathrate structures (in a space group of Im 3 ¯ m) with hydrogenic frameworks. The estimated Tc values exhibit highs of 235 K for CaH6 at 150 [14] GPa and 263~271 K at 300~400 GPa for MgH6 [15]. The ultrahigh Tc values in these systems arise from a substantial DOS value at EF, contributed primarily from hydrogen atoms which comprise the hydrogenic lattices. Therefore, it has been proposed that systems with extended hydrogenic lattices are more likely to become superconductors at higher temperatures. A recent experimental investigation successfully synthesized CaH6 and verified the superconductivity with a measured Tc of 215 K at 172 GPa [16].
Encouraged by the seminal finding in CaH6, extensive theoretical and experimental investigations have been carried out to search for hydrides with extended hydrogenic lattices. The hydrides with d-block elements are typical examples. A large number of scandium, yttrium, and lanthanum hydrides have been predicted to be stable under high pressures, and some of them have had high calculated Tc values. For example, ScH6 was predicted to stabilize in a structure isotypic with CaH6 at pressures above 265 GPa [17]. ScHx (x = 7~10 and 12) was predicted to be synthesized by compressing mixtures of ScH3 and H2 above 150 GPa, forming the Cmcm, Immm, P63/mmc, Cmcm, and C2/c structures, respectively [18,19]. The calculated Tc values of these systems were reported to be 120~169 K at pressures above 250 GPa [19].
Similar to CaH6, theoretical calculations have shown that H clathrate structures could also be formed in rare earth (RE) hydrides such as REH6, REH9, and REH10, where RE = Y, La, Ce, and Pr [4]. These compounds are peculiar, since the H atoms in their structures are weakly covalently bonded with each other, forming unusual H cages with stoichiometries of H24, H29, and H32. The estimated Tc values of these systems are striking [3,4,20]. YH10 and LaH10 (both within the Fm 3 ¯ m symmetry) have been predicted to be potential room temperature superconductors with maximum Tc values of 303~326 K at 250~400 GPa and 274~286 K at 210~250 GPa, respectively [3,4]. Remarkably, some of these materials, consistent with the theoretically predicted structures, have been successfully synthesized in recent experiments [21]. For example, YH6 and YH9 were measured to have Tc values of 220 K at 166 GPa [22] and 243 K at 201 GPa [23], respectively. LaH10 was experimentally synthesized to exhibit a Tc value of 250 K at 170 GPa [6]. Synthesized LaH9 and CeH9 alloys exhibited Tc values of 148~178 K in the pressure range of 97~172 GPa [24]. At much lower pressures, the Tc values of CeH9 (with the Fm 3 ¯ m structure) and CeH10 (with the P63/mmc structure) were measured to be 57 K at 88 GPa and 115 K at 95 GPa [25,26], respectively. However, the theoretically predicted YH10 and its highest Tc > 300 K has not yet been observed in experiments [23].
As the neighbor elements of Sc and Y, the high-pressure structures and superconductivities of titanium (Ti), zirconium (Zr), and hafnium (Hf) hydrides have also been studied. However, these systems have not exhibited good superconducting properties. The ZrH phase with a Cmcm structure and HfH2 phase with a P21/m structure are the only two phases that have been identified to exhibit significant electron–phonon coupling (EPC). The maximum Tc values have been estimated to be 10.6 K for ZrH at 120 GPa [27] and 12.8 K for HfH2 at 260 GPa [28]. In the group V metal hydrides, only the I4/mmm phase of NbH4 has been calculated to have a Tc of 47 K at 300 GPa [29]. The relatively higher Tc in this phase can be traced back to the larger EPC parameter and average logarithmic frequency.
In addition to the above hydrides with metal elements, interesting superconductivity properties have also been discovered in hydrides with non-metal elements. The sulfur hydride is one of the most favorable examples, which has been studied extensively in experiments and calculations.
Theoretical calculations have indicated that H2S is thermodynamically and dynamically stable, up to 200 GPa [30]. The calculated Tc was 80 K in the Cmca-H2S [31]. H3S has been predicted to stabilize in the R3m and Im 3 ¯ m phases at pressures of 111 and 180 GPa, respectively [31]. The two structures both have a particularly high EPC, which leads to high Tc values of 155~166 K at 130 GPa and 191~204 K at 200 GPa [31]. Recent experimental investigations have confirmed the ultrahigh Tc superconductivity in the Im 3 ¯ m phase H3S under high pressure [31]. In addition, high Tc superconductivity has also been predicted in other sulfides. For example, in the H-S-P system (H3S0.925P0.075), the maximum Tc was theoretically estimated to be 280 K at 250 GPa [32]. In the C-S-H system, a Tc of 260 K at 133 GPa was reported in a recent experiment with a modulated AC susceptibility technique adapted for a diamond anvil cell [33]. This experiment revealed a Pnma structure of the material which was responsible for the near room-temperature superconductivity of carbonaceous sulfur hydride at 107–133 GPa [33].
Following the discovery of striking superconductivity in sulfur hydrides, the potential superconductivities of hydrides with isoelectronic selenium (Se) and tellurium (Te) have also been investigated under high pressures. H3Se was predicted to stabilize in the Im 3 ¯ m phase above 200 GPa [34], which is isostructural to H3S. Due to a smaller EPC parameter compared to H3S, DFT calculations yielded a lower Tc value of 130 K for H3Se at 200 GPa [34]. In the Te-H system, the structures and stoichiometries were somehow different from those of sulfur and selenium. DFT calculations showed that P6/mmm-H4Te, C2/m-H5Te2, and P63/mmc-HTe were the most stable phases at 200 GPa [35]. The stoichiometry of H3Te stabilized in a C2/m structure above 300 GPa. The largest Tc in Te-H systems was obtained in the H4Te phase, of which the calculated value was 104 K at 170 GPa [35]. Furthermore, superconductivity has also been reported in some other hydrides. For example, an experimental study indicated that PH3 exhibited superconductivity with a maximum measured Tc of 100 K at 207 GPa [36]. DFT calculations estimated a Tc of 150 K for AsH8 at 350 GPa [37].
As demonstrated by the above investigations, metal hydrides with clathrate structures are a special class of H-rich compounds that may achieve high Tc superconductivity approaching or exceeding room temperature. The reason why they have such a high Tc can be traced back to the combination of a high density of states near EF and strong electron–phonon interactions.
The rare earth element erbium (Er), with partially filled f orbitals, is one of the most reactive metal elements, which results in unique electronic and bonding properties. Under ambient conditions, erbium reacts with hydrogen, consecutively forming metallic ErH2 with a CaF2-type structure and insulating ErH3 with a HoD3-type structure [38]. Recent DFT calculations have demonstrated that ErH2 could be a superconductor with a Tc of ~80 K at 14.5 GPa [39]. If sufficient pressure is applied to ErH3, it can also be forced to be transformed into metallic states. However, no superconductivity has yet been observed for ErH3 in previous theoretical and experimental studies at pressures up to 140 GPa [40,41,42]. In this paper, we perform systematic structure searches by increasing the H concentration in Er-H systems, with the aim of finding clathrate Er hydrides. Encouragingly, we do predict two novel stable clathrate Er hydrides with the stoichiometries of ErH4 and ErH6 in the pressure range of 50~300 GPa. It is found that both of the two clathrate hydrides can achieve high-Tc superconductivity.

2. Methods and Computational Details

The searching simulations of crystal structure with 1~4 formula units in the models of ErHn (n = 4~6) were performed using the swarm-intelligence-based CALYPSO method and software [43,44], which has been successfully applied to predict the structures of many systems [45,46,47,48]. The structure optimizations and electronic property calculations were performed following the plane-wave basis projector-augmented-wave (PAW) method [49] in the framework of density functional theory as implemented in the Vienna ab initio simulation package (VASP) code [50]. In these calculations, the generalized gradient approximation in the Perdew–Burke–Ernzerhof [51] form is applied for the exchange-correlation functionals. The configurations of 5s25p66s24f12 and 1s1 of Er and H, respectively, are treated as valence electrons for the PAW pseudopotentials. The cutoff energy is set to 650 eV, and the Monkhorst–Pack grid with a maximum spacing of 0.03 Å−1 is individually adjusted in reciprocal space to the size of each computational cell. The density functional perturbation theory, as implemented in the Quantum ESPRESSO (QE) package [52], is used to examine the dynamical stability and to calculate the electron–phonon coupling (EPC) parameters of these compounds. The Troullier–Martins norm-conserving scheme is used to generate the pseudopotentials for H and Er, wherein the Er 4f electrons are treated as valence electrons. The Brillouin zone is sampled using a 4 × 4 × 4 q-point grid in the calculations of the EPC parameters. A denser 24 × 24 × 24 k-point mesh is used to accurately calculate the electron–phonon interaction matrix. The kinetic energy cutoffs are set to 70 Ry for the plane wave functions and 600 Ry for the charge density. The formation enthalpies (ΔH) of ErHn are calculated by using: ΔH(ErHn) = H(ErHn) − H(ErH3) − (0.5n − 1.5)H(H2), where H is the enthalpy of the most stable structure of certain compositions at the given pressure. For ErH3, the Fm 3 ¯ m and P63/mmc structures are considered [39], and for elemental H2, the P63/m, C2/c, and Cmca-12 phases are used [53].

3. Results and Discussion

3.1. Crystal Structures and Stabilities

As mentioned in the Introduction, hydrides with high Tc benefit from the clathrate structures. To explore the superconductivity of the Er-H system, first, we search stable structures for ErHn (n = 4~6) at 50~300 GPa. The formation enthalpies (with respect to decomposition into ErH3 and H2) versus composition for the energy favorable structures of each compound are displayed in Figure 1, from which the thermodynamical stability can be obtained. The results show that no compounds are stable at 50 GPa, since all of the formation enthalpies are positive. When the pressure increases to 100 GPa, the formation enthalpies become negative. Meanwhile, ErH4 and ErH6, which locate on the convex hull, become stable. As pressure further increases up to 200 and 300 GPa, ErH4 and ErH6 maintain their stabilities.
Our structure searches show that both ErH4 and ErH6 crystalize in clathrate structures under high pressure. The pressure dependence of the enthalpy difference for the energy low-lying structures are plotted in Figure 2. In the case of ErH6, the clathrate structure stabilizes above 88 GPa and adopts an Im 3 ¯ m symmetry which is similar to that of XH6 (X = Tb, Ca, Mg, Y, and Sc) [12,54]. As shown in Figure 3a, the Im 3 ¯ m-ErH6 forms an H24 cage structure with the Er atoms locating at the cage center. The H24 cage consists of six squares and eight hexagons, and the H-H bond lengths in the both the squares and the hexagons are 1.17, 1.19, 1.21, 1.25, and 1.29 Å at 100, 150, 200, 250, and 300 GPa, respectively. These bond values are smaller than those in TbH6 and CaH6, and larger than those in ScH6 and MgH6 at the same conditions [12,54]. The nearest H-Er distances are 2.04 Å and 1.85 Å at 100, 300 GPa, respectively. The crystal structure parameters of Im 3 ¯ m-ErH6 and the other predicted stable phases are presented in Table 1.
As shown in Figure 3b, the calculated electron localization function (ELF) [55] reveals weakly covalent bonding of H-H in the H24 cage. For example, the value of ELF is 0.59 at 100 GPa. It is worth noting that systems with weak covalent bonds are expected to reach high Tc superconductivity. From this point of view, it is necessary to investigate the superconductivity of Im 3 ¯ m-ErH6.
As revealed in Figure 2, the Im 3 ¯ m phase of ErH6 is stable under pressures of 88~300 GPa. When the pressure decreases to below 88 GPa, it transforms to the P 1 ¯ phase. The H atoms in this phase form two types of H2 units, as displayed in Figure 3d. The H-H bond lengths of the H2 units are 0.97 and 1.44 Å at 80 GPa, respectively. The corresponding ELF (Figure 3e) values are 0.96 and 0.55, respectively, indicating different strengths of covalent bonding.
The phonon dispersions of ErH6 at different pressures are plotted in Figure 4. It is shown that there is no imaginary frequency in the phonon spectra of Im 3 ¯ m-ErH6 at 100 and 300 GPa, indicating that they are dynamically stable (Figure 4a). A prominent feature of the Im 3 ¯ m phase is the drastic softening of the low-lying optical mode around the H point and along the N-Γ and P-N directions when the pressure decreases from 300 to 100 GPa. At 86 GPa, strong phonon softening leads to the emergence of imaginary frequencies at the H point and along the P-N direction, which is responsible for the structural phase transition from Im 3 ¯ m to P 1 ¯ . The dynamical stability of P 1 ¯ -ErH6 is also revealed by the phonon spectra, as presented in Figure 4b.
For ErH4, the clathrate structure is the only thermodynamically stable phase above 50 GPa. This phase shares the same crystal structure of I4/mmm with TbH4 [45]. As presented in Figure 3c, the H atoms in this phase form a cage-like structure of H18, containing eight quadrilaterals and four hexagons. There are two types of H-H bonds in I4/mmm-ErH4, and the bond lengths are 1.36 and 1.39 Å at 300 GPa, and 1.58 and 1.23 Å at 100 GPa, respectively. The corresponding values of ELF (Figure 3f) are 0.52 and 0.45 at 300 GPa, and 0.41 and 0.73 at 100 GPa, respectively. This result indicates that the H-H covalent bonds present opposite responses of compression, i.e., the former is strengthened by pressure and the latter is weakened. The dynamical stability of this phase can also be demonstrated by the phonon dispersions presented in Figure 4c.

3.2. Electronic Characteristics and Superconductivity

To analyze the electronic properties of ErHn, we calculate the electronic density of states (DOS). Our results indicate that all the stable Er-H phases predicted here exhibit metallic nature in the corresponding stable pressure range. It is worth noting that even crystallized in different structures, the DOS distributions of Im 3 ¯ m-ErH6, P 1 ¯ -ErH6, and I4/mmm-ErH4 bear strong resemblance to each other. As shown in Figure 5, the projected DOS on different orbitals of Er and H atoms all cross at the Fermi level. The electronic states around the Fermi level are mainly contributed from Er-f, Er-d, and H-s orbits, while the contribution of Er-s and Er-p are relatively scanty. Another overall feature of the DOS results is the broadening of Er-f electronic states, indicating that the 4f electrons are delocalized and the electronic correlation effect is weakened by pressure.
To assess the superconductivity of the Er-H systems, the Eliashberg electron–phonon spectral function [α2F(ω)], the EPC parameter (λ), and the logarithmic average of phonon frequency (ωlog) are then calculated. As shown in Figure 6, for Im 3 ¯ m-ErH6, the EPC parameters are calculated to be 3.89 and 1.60 at 100 and 300 GPa, respectively. The corresponding values of ωlog are 857.4 K and 1427.8 K, respectively. The vibrations of H atoms which dominate the medium- and high-frequency region in the phonon DOS contribute 84% and 80% to the total EPC at 100 and 300 GPa, respectively. The strong EPC of this phase at low pressure is attributed to the strong phonon softening (Figure 4). For P 1 ¯ -ErH6, the absence of H cage structure leads to a much weaker EPC of λ = 0.48 at 80 GPa. However, the ωlog still has a considerable value of 944.8 K at this pressure, attributing to the high content of H. Different from the Im 3 ¯ m phase, the contribution of H-atom vibrations located in the medium frequency (15~46 THz) contribute mainly (75%) to the total EPC in the P 1 ¯ -ErH6. The contribution of high-frequency vibrations is only 3%.
In the case of I4/mmm-ErH4, the electron–phonon interaction is also considerable. The calculated values of λ are 0.96 and 0.85 at 150 and 300 GPa, respectively, and the corresponding ωlog values are 1231.7 and 1379.9 K, respectively. Similar to Im 3 ¯ m-ErH6, the vibrations of H atoms both in the medium- and high-frequency region contribute dominantly to the total EPC.
Based on the above data combined with a typical Coulomb pseudopotential value of µ* = 0.1, the superconducting critical temperature (Tc) values can be estimated in terms of the Allen–Dynes modified McMillan equation [56]. The obtained Tc of Im 3 ¯ m-ErH6 reaches high values of 130.9 K and 181.2 K at 100 GPa and 300 GPa, respectively. However, the P 1 ¯ -ErH6 has a much lower Tc of 9.3 K at 80 GPa, because of the absence of H cage structure. For I4/mmm-ErH4, the EPC is relatively weak and the resultant Tc values are 74.4 K and 79.8 K at 150 GPa and 300 GPa, respectively. This result indicates that the cage structure of H atoms obviously leads to higher superconducting critical temperatures, which is consistent with the perspectives of Zurek et al [57].

4. Conclusions

In summary, we have predicted two new Er hydrides with the stoichiometries of ErH4 and ErH6, using the CALYPSO crystal structure prediction method combined with first-principles calculations. ErH4 was predicted to crystalize in a clathrate structure in the whole pressure range considered here. This phase has a space group of I4/mmm, wherein the H atoms bond to each other and form H18 cages. ErH6 was also predicted to stabilize in a clathrate structure with the space group of Im 3 ¯ m at pressures above 88 GPa. In this phase, the H atoms form a H24 cage sublattice. As pressure decreases to below 88 GPa, the Im 3 ¯ m phase transforms to a low symmetrical phase with a space group of P 1 ¯ , attributed to the strong phonon softening. All of the predicted phases exhibit good metallic nature at their stable pressure ranges. The estimated maximum value of Tc in the Er-H system is obtained in the Im 3 ¯ m phase of ErH6, which reaches a high value of 181.2 K at 300 GPa. Our results enrich the family of rare earth hydrides and may help with the further discovery of room temperature superconductors in metal hydrides.

Author Contributions

Conceptualization, X.Z.Y. and Y.M.C.; investigation, X.Z.Y., Z.L.Z., Y.M.C. and F.G.K.; data curation, X.Z.Y. and Z.L.Z.; writing—original draft preparation, X.Z.Y.; writing—review and editing, X.Z.Y. All authors have read and agreed to the published version of the manuscript.


This work is supported by the National Natural Science Foundation of China under grant nos. 11704163, 11804131, and 11964001; the Educational Commission of Jiangxi Province of China under grant no. GJJ200862; the Natural Science Foundation of Jiangxi Province of China under grant no. 20181BAB211007.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.


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Figure 1. Enthalpies of ErHn formation (n = 4~6) at 50~300 GPa. The solid symbols connected by solid lines on the convex hull denote the stable phases against any type of decomposition. The open symbols located above the convex hull represent unstable or metastable phases. The colorful dotted and black dashed lines are for the eye-guide only.
Figure 1. Enthalpies of ErHn formation (n = 4~6) at 50~300 GPa. The solid symbols connected by solid lines on the convex hull denote the stable phases against any type of decomposition. The open symbols located above the convex hull represent unstable or metastable phases. The colorful dotted and black dashed lines are for the eye-guide only.
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Figure 2. Pressure dependence of the enthalpy difference for the energy low-lying structures of: (a) ErH6; (b) ErH4.
Figure 2. Pressure dependence of the enthalpy difference for the energy low-lying structures of: (a) ErH6; (b) ErH4.
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Figure 3. Crystal structures and bonding properties: (a) Structure of Im 3 ¯ m-ErH6; (b) ELF of Im 3 ¯ m-ErH6 at 100 GPa; (c) structure of I4/mmm-ErH4; (d) structure of P 1 ¯ -ErH6; (e) ELF of P 1 ¯ -ErH6 at 80 GPa; (f) ELF of I4/mmm-ErH4 at 100 GPa. The isosurface value of ELF is set to 0.5. Small and large spheres denote H and Er atoms, respectively.
Figure 3. Crystal structures and bonding properties: (a) Structure of Im 3 ¯ m-ErH6; (b) ELF of Im 3 ¯ m-ErH6 at 100 GPa; (c) structure of I4/mmm-ErH4; (d) structure of P 1 ¯ -ErH6; (e) ELF of P 1 ¯ -ErH6 at 80 GPa; (f) ELF of I4/mmm-ErH4 at 100 GPa. The isosurface value of ELF is set to 0.5. Small and large spheres denote H and Er atoms, respectively.
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Figure 4. Phonon dispersions of: (a) Im 3 ¯ m-ErH6 at 100 GPa (dotted line) and 300 GPa (solid line); (b) P 1 ¯ -ErH6 at 80 GPa; (c) I4/mmm-ErH4 at 150 (dotted line) and 300 GPa (solid line), respectively.
Figure 4. Phonon dispersions of: (a) Im 3 ¯ m-ErH6 at 100 GPa (dotted line) and 300 GPa (solid line); (b) P 1 ¯ -ErH6 at 80 GPa; (c) I4/mmm-ErH4 at 150 (dotted line) and 300 GPa (solid line), respectively.
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Figure 5. Projected density of states (DOS) of: (a) Im 3 ¯ m-ErH6 at 100 GPa; (b) P 1 ¯ -ErH6 at 80 GPa; (c) I4/mmm-ErH4 at 100 GPa. The Fermi energy is set at 0 eV.
Figure 5. Projected density of states (DOS) of: (a) Im 3 ¯ m-ErH6 at 100 GPa; (b) P 1 ¯ -ErH6 at 80 GPa; (c) I4/mmm-ErH4 at 100 GPa. The Fermi energy is set at 0 eV.
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Figure 6. Eliashberg electron–phonon spectral function α2F(ω) (solid line), the integral EPC parameter λ (dashed line) as a function of frequency, and the corresponding phonon DOS (dash area) of (a) Im 3 ¯ m-ErH6 at 300 GPa; (b) Im 3 ¯  m-ErH6 at 100 GPa; (c) P 1 ¯ -ErH6 at 80 GPa; (d) I4/mmm-ErH4 at 150 GPa.
Figure 6. Eliashberg electron–phonon spectral function α2F(ω) (solid line), the integral EPC parameter λ (dashed line) as a function of frequency, and the corresponding phonon DOS (dash area) of (a) Im 3 ¯ m-ErH6 at 300 GPa; (b) Im 3 ¯  m-ErH6 at 100 GPa; (c) P 1 ¯ -ErH6 at 80 GPa; (d) I4/mmm-ErH4 at 150 GPa.
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Table 1. Crystal lattice parameters of the predicted stable ErHn phases under high pressures.
Table 1. Crystal lattice parameters of the predicted stable ErHn phases under high pressures.
PhasePressure (GPa)Lattice ParametersCoordinates
Im 3 ¯ m-ErH6100a = 3.16 Å α = 109.47
b = 3.16 Å β = 109.47
c = 3.16 Å γ = 109.47
H1 0.25000 0.50000 −0.25000
Er1 0.00000 0.00000 0.00000
P 1 ¯ -ErH680a = 3.15 Å α = 89.99
b = 3.67 Å β = 100.40
c = 4.71 Å γ = 89.99
H1 0.82939 0.51335 0.88270
H2 0.78475 0.54530 0.67573
H3 0.36777 0.74998 0.87671
H5 0.72069 0.24999 0.43394
H6 0.82940 0.98659 0.88268
H7 0.78476 0.95469 0.67571
Er1 0.29653 0.24999 0.73683
I4/mmm-ErH4100a = 3.31 Å α = 129.59
b = 3.31 Å β = 129.59
c = 3.31 Å γ = 74.05
H1 1.38370 1.38370 1.00000
H2 0.75000 1.25000 0.50000
Er1 0.00000 0.00000 0.00000
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Yan, X.Z.; Zhang, Z.L.; Chen, Y.M.; Kuang, F.G. Prediction of Superconductivity in Clathrate Er Hydrides under High Pressure. Crystals 2023, 13, 792.

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Yan XZ, Zhang ZL, Chen YM, Kuang FG. Prediction of Superconductivity in Clathrate Er Hydrides under High Pressure. Crystals. 2023; 13(5):792.

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Yan, Xiao Z., Zhao L. Zhang, Yang M. Chen, and Fang G. Kuang. 2023. "Prediction of Superconductivity in Clathrate Er Hydrides under High Pressure" Crystals 13, no. 5: 792.

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