LaThH 10 the potential high- Tcsuperconductors stabilized thermodynamically below 200 GPa Peng Song1Zhufeng Hou2Kenta Hongo3and Ryo Maezono1 1School of Information Science JAIST Asahidai 1-1 Nomi Ishikawa 923-1292 Japan

2025-04-27 0 0 9.65MB 25 页 10玖币

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(La,Th)H10: the potential high-Tcsuperconductors stabilized thermodynamically below 200 GPa

Peng Song,1Zhufeng Hou,2Kenta Hongo,3and Ryo Maezono1

1School of Information Science, JAIST, Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan

2State Key Laboratory of Structural Chemistry, Fujian Institute of Research on

the Structure of Matter, Chinese Academy of Sciences, Fuzhou 350002, China

3Research Center for Advanced Computing Infrastructure,

JAIST, Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan

(Dated: October 19, 2022)

The recent high-pressure experimental discovery of superconductivity in (La,Y)H10, (La,Ce)H9, (La,Ce)H10,

(Y,Ce)H9, and (La,Nd)H10 shows that the ternary rare-earth clathrate hydride can be promising candidate for

high-temperature superconductor. In this work, we theoretically demonstrate that the combination of actinide-

metal thorium (Th) and rare-earth-metal lanthanum (La) with hydrogen can also form some ternary hydrides

with cage-like structures to be stable at 200 GPa. Using the evolutionary algorithms combined with the ﬁrst-

principles calculations, we have predicted the pressure-dependent ternary phase diagram of LaxThyHz, partic-

ularly including the case of (La1−xThx)Hn[or designated as (La,Th)Hnfor simplicity]. Our calculations show

that the hydrogen-rich phases such as (La,Th)H9(only including P¯

6m2-LaThH18) and (La,Th)H10 (including

I4/mmm-La3ThH40,R¯

3m-LaThH20, and I4/mmm-LaTh3H40) with H29 and H32 cages can be thermodynamically

stable below 200 GPa. However, the phase decomposition can happen to only (La,Th)H9when the pressure is

above 150 GPa. More importantly, the electron-phonon coupling (EPC) calculations show that the (La,Th)H10

series could the potential superconductors, of which I4/mmm-La3ThH40 at 200 GPa exhibits the large EPC

constant λ=2.46 with a highest transition temperature (Tc) of 210 K. Since there are few previous studies on

ternary hydrides composed of actinide metals, the present work would greatly stimulate the further discovery of

this type of ternary hydrides and provide useful guidance for the high-pressure experimental studies on them.

I. INTRODUCTION

The current progress of the theoretical studies on high-

pressure superconducting hydrides has reached an unprece-

dented stage, with the resolution of almost all binary hy-

drides and some ternary and multiple hydrides. [1–4] The

superconducting transition temperatures (Tc) of the H-cage-

containing hydrides such as MgH6, YH6, YH9, YH10, LaH10,

Li2MgH16, and LaYH20 have been predicted to be close to

or even greater than the room temperature. [5–9] The near-

room-temperature superconductivity in lanthanum hydride

and lanthanum-yttrium ternary hydrides has been demon-

strated in high-pressure experiments with the XRD diﬀraction

measurements to conﬁrm their crystal structures. [9–11]

Most of the high-temperature superconducting hydrides

synthesized currently in experiment are crystalized in the

hydrogen clathrate structure composed of alkaline-earth and

rare-earth metals. [9–19] The presence of hydrogen in the

form of cage structures, which could potentially reduce the

product of pressure and volume (PV) for its contribution to

enthalpy, is one of the fundamental factors to stabilize these

clathrates at lower pressure. Thanks to the signiﬁcant H-

derived electron density of states at the Fermi level and the

robust electron-phonon coupling associated with the weak

bonding of H atoms inside the cage, the cage structures of

metal hydrides have been predicted to exhibit potential high-

temperature superconductivity. [6,8,20] For the rare-earth

clathrates that have been predicted by theoretical calculations

to have superconductivity, not all of them have been veriﬁed

by high-pressure measurements. One of the plausible rea-

sons may be ascribed to the signiﬁcant magnetic characteris-

tics. [6,21–24] The noteworthy thing is that high-temperature

superconductivity can be preserved in the sodalite-like struc-

tures, which could be formed by substituting carbon and/or

nitrogen for hydrogen in clathrates, as reported in very recent

theoretical calculations. [25–29] Besides, a thermodynami-

cally stable carbon-boron sp3-bonded clathrate determined by

particle-swarm structure prediction approach was successfully

synthesized by Zhu et al. [30] These studies illustrate that the

high-temperature superconductivity in metal hydrides exhibits

a strong correlation with the clathrate structure.

Recently, the superconductivity of ternary clathrate hy-

dride has also attracted a lot of attention, and most of them

cover the hydrides of alkaline-earth metals and rare-earth met-

als. [9,31–41] Although the theoretically predicted Tcof

Li2MgH16 composed of alkali and alkaline-earth metals at 250

GPa is 473 K, its enthalpy of formation lies above the con-

vex hull [8,42] and its synthesis in experiment is still a great

challenge. It is noteworthy to mention that partial replace-

ment of La atoms by magnetic Nd atoms results in signiﬁcant

suppression of superconductivity in LaH10. [41] This provides

a hint to design new superconducting materials. Among the

ternary hydrides with cage structures, we note that some of

their speciﬁc compositions such as (A,B)H6, (A,B)H9, and

(A,B)H10 can be obtained by mixing their parent compounds

(AHxand BHx,x=6, 9, and 10) with the same cage struc-

tures. [9,31,35–37] The ground state electron conﬁgurations

of La and Th are [Xe]5d16s2and [Rn]5d27s2. Their elec-

tronegativity and atomic radius are quite close to each other.

More interestingly, both of them can form the stable binary

hydride Fm¯

3m-AH10 at pressure lower than 200 GPa, [7,43]

which have also been conﬁrmed in experiment. [10,11,13] It

is natural for us to consider whether (La,Th)H10 could be sta-

ble or not. If so, the chemical synthesis of (La,Th)H10 would

be straightforward and also similar to that of (La,Y)H10 [9].

Therefore, we concentrate on the ternary compounds of La-

arXiv:2210.06371v2 [cond-mat.supr-con] 18 Oct 2022

Th-H and their structural stability as well as superconductiv-

ity.

In this work, we have systematically investigated the sta-

bility and superconductivity of LaxThyHzunder high pres-

sure using the ﬁrst-principles calculations combined with the

evolutionary algorithms for structure search. The hydrogen-

rich phases such as I4/mmm-La3ThH40,R¯

3m-LaThH20, and

I4/mmm-LaTh3H40 are found to be stabilized below 200 GPa

and all of them exhibit potential high-temperature supercon-

ductivity. In particular, I4/mmm-La3ThH40 at 200 GPa is pre-

dicted to have a highest Tcof 210 K.

II. METHOD

The structure search for LaxThyHzwas performed using

the evolutionary variable-composition simulation as imple-

mented in the USPEX (Universal structure predictor: evolu-

tionary Xtallography) software [44,45]. The crystal struc-

tures of LaxThyHzwere considered with a maximum number

of 24 atoms per cell at a series of ﬁxed pressure including

5, 50, 100, and 200 GPa. 200 structures in the ﬁrst genera-

tion were created randomly, while 100 structures in the sub-

sequent every generation were obtained by four diﬀerent ma-

nipulations, namely, 40% by hereditary, 40% by random cre-

ation, 10% by mutation, and 10% by soft mutation. A total

of 100 generations were iterated for each considered compo-

sition of LaxThyHz. Since the high-temperature superconduc-

tivity is usually observed in hydrogen-rich materials, herein

we omitted the composition of (x+y)/z<1 by the seed

technique [45] in USPEX. To further check whether the stable

phase may have a maximum number of more than 24 atoms

per cell or not, we carried out a speciﬁc structure search for

the (LaH10)x0(ThH10)y0system under the pressure of 100 and

200 GPa. Each structure underwent a four-round optimization

by the ﬁrst-principles calculations, which were carried out us-

ing the VASP (Vienna ab initio software package) [46–49]

code. A force convergence criterion of 0.02 eV/Å was speci-

ﬁed in the last round of optimization. The interaction between

ions and electrons was described by the projector augmented

waves (PAW) method [50,51] and the recommended PAW po-

tentials for La, Th, and H were employed. The cutoﬀenergy

of 600 eV was used for the plane-wave basis-set. The Perdew-

Burke-Ernzerhof (PBE) exchange-correlation functional [52]

was employed. The k-points in the ﬁrst Brillouin zone (BZ)

were sampled with a setup of 0.1 Å−1for the smallest allowed

spacing between k-points.

Based on the enthalpies of LaxThyHzobtained by the VASP

calculations, the convex hull construction for the LaxThyHz

phase diagram was determined using the Pymatgen [53] tool.

The enthalpy of a phase above the convex hull indicates that

such a phase is unstable and thus it would be decomposed into

other phases.

For the stable phases of LaxThyHz, their phonon disper-

sions and superconductivity were calculated within the den-

sity functional perturbation theory (DFPT) [54] as imple-

mented in Quantum ESPRESSO (QE) [55] code. The plane

wave expansion of the electron eigenstates had a cutoﬀof 113

Ry. In particular, the PAW potenitals of La and Th were gener-

ated according to the valence conﬁgurations of 4f05d16s26p0

and 6d17s27p05f1, respectively. The PBE functional [52]

was used too. The superconducting transition temperature

Tcis evaluated by the Allen-Dynes-modiﬁed McMillan for-

mula [56]:

Tc=ωlog f1f2

1.2exp −1.04(1 +λ)

λ(1 −0.62µ∗)−µ∗!,(1)

with

f1f2=3

s1+"λ

2.46(1 +3.8µ∗))#3

×"1−λ2(1 −ω2/ωlog)

λ2+3.312(1 +6.3µ∗)2#,(2)

where µ∗is the Coulomb pseudopotential parameter. The

widely accepted value of 0.1 for µ∗is used herein. The

electron-phonon coupling constant λ, logarithmic average

phonon frequency ωlog, and mean square frequency ω2are

deﬁned as below

λ=2Zα2F(ω)

ωdω, (3)

ωlog =exp "2

λZdω

ωα2F(ω)logω#,(4)

and

ω2=s1

λZ"2α2F(ω)

ω#ω2dω, (5)

respectively. In the case of f1f2=1, the Allen-Dynes-

modiﬁed McMillan formula is restored to the original McMil-

lan formula [57].

III. RESULTS

A. Thermodynamic Stability and crystal structure of La-Th-H

system

The convex hulls for the stable and metalstable phases of

LaxThyHzat the pressure of 5, 50, 100, and 200 GPa are pre-

sented in Fig. 1. The complete information about the enthalpy

of formation and structure properties of these phases is listed

in Table S1-S5 in the Supporting Information (SI). There is

no stable ternary phase in the phase diagram of LaxThyHz

at ambient pressure, which is easily accessible through the

Materials Project (MP) database [58,59]. The binary hy-

drides of both La and Th at ambient pressure have been ex-

tensively studied in experiment [60] and theoretical calcula-

tions [61,62]. It is worth noting that Th4H15 has been synthe-

sized and also found to be a superconductor at low pressure

(5 GPa). [63] Our calculations show that at 5 GPa there is a

stable ternary phase, i.e., Pm¯

3-LaThH6. For the Th-H binary

phase, our calculations predict a new stable phase, i.e., R¯

3c-

ThH3, with a lower energy than 3

7ThH2+1

7Th4H15, which has

not been found in previous study [43]. At 50 GPa, our pre-

dicted binary phases are in overall agreement with those re-

ported in previous studies [6,43,64]. For the ternary case, the

low-symmetry Cm-LaTh2H10 is found to be also stabilized at

50 GPa beside Pm¯

3-LaThH6. At 100 GPa, Pm¯

3-LaThH6be-

comes unstable, while more new stable phases appear along

(LaH4)x0(ThH4)y0line. We should point out that the Fmmm-

LaTh2H12 phase is just located at 0.04 meV/atom above the

convex hull, which could also be stabilized owing to such

a tiny energy. Although LaH9is a metastable phase at 100

GPa, P¯

6m2-LaThH18 is a stable ternary hydrogen-rich phase

emerging along (LaH9)x0(ThH9)y0. When the pressure is fur-

ther increased to 200 GPa, most of the stable phases with com-

positions along (LaH4)x0(ThH4)y0at 100 GPa still remain on

the convex hull except Pmmm-La3ThH16. Phase decomposi-

tion happens to P¯

6m2-LaThH18 at 200 GPa. Supplementary

structure search at 200 GPa was carried out speciﬁcally for the

compositions along (LaH10)x0(ThH10)y0line. In this way, sev-

eral novel hydrogen-rich phases such as I4/mmm-La3ThH40,

R¯

3m-LaThH20, and I4/mmm-LaTh3H40 were found to be ther-

modynamically stable. In addition, Immm-LaTh2H30 is lo-

cated at 0.2 meV/atom above the convex hull and thus it is

also extremely close to stable phase.

The crystal structures for the predicted stable phases of

LaxThyHzare shown in Fig. 2. Except for Pm¯

3-LaThH6

and Cm-LaTh2H10, which are stable below 50 GPa, the rest

of the predicted stable phases of (La,Th)H4, (La,Th)9, and

(La,Th)H10 take the clathrate structures composed of H18,

H29, and H32 cages, respectively. The H18, H29, and H32 cages

consist of a dodecahedron (8 eight quadrangle and 4 hexag-

onal faces), a dodecahedron (12 pentagonal and 6 quadran-

gle faces), and an octahedron (12 hexagonal and 6 quadran-

gle faces), respectively. The similar clathrate structures have

been extensively studied in hydrogen storage materials [65].

The binary hydrides with clathrate structures have been pre-

dicted to possess excellent superconducting properties. [6,43]

Although the (La,Th)H4with several diﬀerent compositions

(i.e., the La/Th ratios) would undergo phase transition from

100 GPa to 200 GPa, the same H18 cage structure is kept

during the pressure-induced phase transition. This is because

these cage structures are more competitively stable under high

pressure because of the relatively reduced contribution of PV

term to enthalpy. [6]

From ambient pressure to high pressure, the thermody-

namically stable phases of LaxThyHzare gathered mainly

on four lines, i.e., (La,Th)H3, (La,Th)H4, (La,Th)H9, and

(La,Th)H10), as seen from Fig. 2. The shortest decomposi-

tion path of LaThH6and LaThH18 was determined using the

Pymatgen [53] tool. The decomposition reaction of LaThH6

at 100 GPa is LaThH6→1

3La +ThH4+2

3LaH3, and hence

the applying more high pressure to LaThH6would not obtain

a new ternary phase. Similarly, the decomposition reaction of

LaThH18 at 200 GPa is LaThH18 →1

6LaTh3H40 +1

2LaThH20

3LaH4. From the two main contributions (i.e., internal

energy and PV) to the pressure-dependent relative enthalpy

of LaThH18 given with respect to the decomposed phases,

as shown in Fig. S1 in the SI, it is found that the contribu-

tion from PV plays a more signiﬁcant role in the pressure-

dependent relative enthalpy, while the one from internal en-

ergy almost remains unchanged.

For the newly predicted ternary phases in the pressure range

of their thermodynamical stabilization, we have checked their

electronic properties including the electronic band structure

and partial density of states (PDOS). The results are presented

in Fig. S2 in the SI. All of these studied LaxThyHzphases ex-

hibit metallic behavior. The electronic states at the Fermi level

(EF) of these phases are strongly dependent on the hydrogen

content. The contribution of H atoms to the electronic states at

EFis nearly zero in LaThH6and LaTh2H10, and it is also neg-

ligible in the (La,Th)H4system, suggesting that the electronic

structures of these phases may be manifested mainly through

La-Th. A previous experiment study showed that the observed

Tcof the La-Th alloy (i.e., Tcbelow 6 K) decreased with in-

creasing Th content. [66] This implies that high-temperature

superconductivity may not be achieved in the aforementioned

phases with lower H content. It is worth noting that the hy-

drogen fraction of the total DOS at EF(denoted as HDOS)

is high in (La,Th)H9and (La,Th)H10. According to Belli et

al. [67], superconducting Tcin hydrides maintains a strong

positive correlation with both HDOS and electron localization

function (ELF) value. According to this argument, (La,Th)H9

and (La,Th)H10 might be potential high-temperature super-

conductors and more detailed results are given in next sub-

section.

B. Phonon dispersion and superconductivity of newly

predicted LaxThyHzphase under the harmonic approximation

We further examine the lattice-dynamic stability and super-

conductivity of these thermodynamically stable phases in the

studied pressure range (5-200 GPa) by performing the phonon

and electron-phonon coupling (EPC) calculations under the

harmonic approximation. It is found that Fmmm-LaTh2H12,

P¯

6m2-LaThH18,Pmmn-LaThH8, and P2/m-LaTh3H16,ex-

hibit phonon with imaginary frequencies, indicting that they

are dynamically unstable, while the remaining thermodynam-

ically stable phases do not. For the phases that meet both ther-

modynamic stability and lattice-dynamic stability, we further

calculated their Eliashberg phonon spectral function α2F. By

integrating α2F, we obtained the EPC constant and then eval-

uated the Tcvalues. The main results are summarized in Ta-

ble I. For the phase with lower H content, the (La,Th)H3and

(La,Th)H4systems are unable to attain high temperature su-

perconductivity due to their low EPC constants. Herein we

take Pm¯

3-LaThH6as an example. The EPC constant of Pm¯

LaThH6is 0.23 and its contribution from the vibration modes

of H atoms is just 0.09 (i.e., accounting for 39%). The low-

symmetry phase P1-La3ThH16 with the highest Tcamong the

(La,Th)H3and (La,Th)H4systems has a signiﬁcant increase

in HDOS and its EPC constant (λ=0.68), of which the contri-

bution from the vibrational modes of H atoms (i.e., account-

ing for 70%). For the phases with much higher H content,

the contribution of H atoms to the electronic density of states

at EFis dominant, so we next focus on the superconductivity

of three hydrogen-rich phases, namely, I4/mmm-La3ThH40,

R¯

3m-LaThH20, and I4/mmm-LaTh3H40.

Figure 3shows the phonon dispersion with a mode-

revolved EPC constant λqν, phonon density of states

(PHDOS), and electron-phonon Eliashberg spectral func-

tion α2F(ω) for I4/mmm-La3ThH40,R¯

3m-LaThH20, and

I4/mmm-LaTh3H40. The EPC constants of these three phases

are 2.46, 1.50, and 1.41, respectively, which follow the sim-

ilar descending order for the density of states at the Fermi

level (NEF). The vibrational modes of phonons of these three

phases can be clearly grouped into two regions according to

the frequencies. The ﬁrst region with phonon frequencies

of 0-10 THz (denoted as region I) is dominated by the vi-

bration modes of La and Th atoms. For the contribution of

phonon in this region to the EPC constants, it is about 0.07

in both LaThH20 and LaTh3H40, while it is high up to 0.33

in La3ThH40. As seen from the mode-revolved EPC λqν,

La3ThH40 shows a signiﬁcant enhancement in EPC along the

path of Z-Σ1-N in its ﬁrst BZ. The second region with phonon

frequencies of ≥10 Thz (denoted as region II) arise from the

vibrational modes of H atoms. The contributions of this re-

gion in the EPC constant are 2.12 (86.5%), 1.41 (94.8%), and

1.34 (94.6%), respectively. The phonon vibrational modes

of La3ThH40 exhibit signiﬁcant softening in the region II es-

pecially at the Σpoint and in the path of Z-Σ1-N. It can be

seen from λqνthat the softened phonon modes with frequen-

cies of 10-20 Thz for La3ThH40 provides a large contribu-

tion (about 0.66) to the EPC constant. Therefore, the diﬀer-

ence in the EPC constants of these three hydrogen-rich phases

is mainly caused by the appearance of the softened modes

in La3ThH40. Based on the Allen-Dynes formula, the high-

est Tcvalue is predicted to I4/mmm-La3ThH40 at 200 GPa,

namely, Tc'210 K when the typical Coulomb pseudopo-

tential parameter µ∗is taken as 0.1. The predicted Tcvalues

of La3ThH40, LaThH20, and LaTh3Th40 via the Allen-Dynes

formula are slightly higher than the respective ones obtained

by the McMillan formula. For LaH10 and ThH10 as the par-

ent compounds of these three superconducting ternary phases,

their predicted Tcvalues with the correction using a strong

coupling factor f1f2are much close to the experimentally

measured ones. I4/mmm-La3ThH40 possesses a higher EPC

constant than its parent compounds, and thus its predicted Tc

value with the same correction is signiﬁcantly lifted.

IV. CONCLUSION

In summary, we have employed the evolutionary algorithms

and the ﬁrst-principles calculations to explore the ternary

phase diagram of the La-Th-H system in the pressure range

over 5 to 200 GPa. It was found that the hydrogen-rich ma-

terials (La,Th)H9(only including LaThH18) and (La,Th)H10

(including La3ThH40, LaThH20, and LaTh3H40) are thermo-

dynamically stable below 200 GPa. When the pressure is

above 150 GPa, LaThH18 would decompose into LaTh3H40,

LaThH20, and LaH4. La3ThH40 with the space group of

I4/mmm is predicted to have a largest EPC constant (i.e.,

λ=2.46) at 200 GPa among these stable phases of La-Th-

H and thus to obtain a maximum superconducting transition

temperature of 210 K. The ternary clathrate hydrides of La-

Ce-H, Y-Ce-H, and La-Y-H have already been synthesized

in high-pressure experiments. La-Th-H exhibits the similar

structural properties to the aforementioned three systems, sug-

gesting that the La-Th-H system would be a promising ideal

candidate to discover new high-temperature superconductor

in high-pressure experiment.

ACKNOWLEDGMENTS

The computations in this work have been performed us-

ing the facilities of Research Center for Advanced Com-

puting Infrastructure (RCACI) at JAIST. K.H. is grate-

ful for ﬁnancial support from the HPCI System Re-

search Project (Project ID: hp190169) and MEXT-KAKENHI

(JP16H06439, JP17K17762, JP19K05029, and JP19H05169).

R.M. is grateful for ﬁnancial supports from MEXT-

KAKENHI (19H04692 and 16KK0097), FLAGSHIP2020

(project nos. hp1 90169 and hp190167 at K-computer), Toy-

ota Motor Corporation, I-O DATA Foundation, the Air Force

Oﬃce of Scientiﬁc Research (AFOSR-AOARD/FA2386-17-

1-4049;FA2386-19-1-4015), and JSPS Bilateral Joint Projects

(with India DST).

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(La,Th)H10:thepotentialhigh-Tcsuperconductorsstabilizedthermodynamicallybelow200GPaPengSong,1ZhufengHou,2KentaHongo,3andRyoMaezono11SchoolofInformationScience,JAIST,Asahidai1-1,Nomi,Ishikawa923-1292,Japan2StateKeyLaboratoryofStructuralChemistry,FujianInstituteofResearchontheStructureofMatter,Chinese...

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LaThH 10 the potential high- Tcsuperconductors stabilized thermodynamically below 200 GPa Peng Song1Zhufeng Hou2Kenta Hongo3and Ryo Maezono1 1School of Information Science JAIST Asahidai 1-1 Nomi Ishikawa 923-1292 Japan.pdf

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LaThH 10 the potential high- Tcsuperconductors stabilized thermodynamically below 200 GPa Peng Song1Zhufeng Hou2Kenta Hongo3and Ryo Maezono1 1School of Information Science JAIST Asahidai 1-1 Nomi Ishikawa 923-1292 Japan

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