Metal-Bonded Perovskite Lead Hydride as a Phonon-Mediated Superconductor up to
46 K under Atmospheric Pressure
Yong He,1 Juan Du,2, ∗ Shi-ming Liu,1 Chong Tian,1 Wen-hui Guo,1 Min
Zhang,3 Yao-hui Zhu,4 Hong-xia Zhong,5 Xinqiang Wang,1 and Jun-jie Shi1, †
arXiv:2302.05263v1 [cond-mat.supr-con] 10 Feb 2023
1
State Key Laboratory for Artificial Microstructures and Mesoscopic Physics, School of Physics, Peking
University Yangtze Delta Institute of Optoelectronics, Peking University, Beijing 100871, China
2
Department of Physics and Optoelectronic Engineering Faculty of
Science, Beijing University of Technology, Beijing 100124, China
3
Inner Mongolia Key Laboratory for Physics and Chemistry of Functional Materials, College
of Physics and Electronic Information, Inner Mongolia Normal University, Hohhot 010022, China
4
Physics Department, Beijing Technology and Business University, Beijing 100048, China
5
School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China
(Dated: February 13, 2023)
With the motivation of searching high-temperature superconductivity in hydrides, numerously
hydrogen-dominated superconductors have been predicted theoretically and some of them have been
also synthesized experimentally at an ultrahigh pressure about several hundred GPa, which is too
high to be used in practical application. To address this issue, we report a new lead hydride, defined
as binary metal-bonded perovskite Pb4 H, featured with better ductility than the widely investigated
multi-hydrogen, iron-based and cuprate superconductors. Structural stability of Pb4 H has been
carefully verified. The Pb4 H presents high critical temperature up to 46 K at ambient pressure,
approximately six times larger than that of bulk Pb, by means of advanced Migdal-Eliashberg
theory. Moreover, the electron-phonon coupling strength of Pb4 H has an enhancement of 58%
than that of bulk Pb because the hydrogen implantation in bulk Pb can induce several new highfrequency optical phonon branches strongly coupled with electrons on Fermi surface, heightening
the superconductivity. Furthermore, Pb4 H is a phonon-mediated two-band superconductor, similar
to metal lead.
I.
INTRODUCTION
The long-sought goal of searching high-temperature superconductors has been regraded as a grand challenge
in condensed matter physics since the discovery of superconductivity Tc =4.15 K in mercury [1]. In 1957,
Bardeen, Cooper and Schrieffer (BCS) proposed a microscopic theory to perfectly explain the superconducting mechanism [2]. Their theory predicted that the critical temperature is proportional to Debye temperature,
which reveals that the light-element compounds possibly exhibit high-temperature superconductivity because
of its high-frequency phonons. In 1968, Ashcroft intuitively suggested that realization of molecule hydrogen
metalization under extremely high pressure should have
the highest transition temperature [3]. With the help
of structural search method and advanced experiments,
numerous phases of solid hydrogen have been predicted
and some of them have been synthesized [4–7]. For example, McMahon et al. predicted the highest Tc at 764 K
in metallic hydrogen under 1-1.5 TPa [4]. However, it is
regrettable that the metallization of solid hydrogen has
not been realized in experiment until now and such high
pressure extremely hinders its investigation in laboratory
and practical application in the future.
To circumvent this problem, Ashcroft further proposed
∗
†
dujuan1121@bjut.edu.cn
jjshi@pku.edu.cn
that the chemical precompression, contributed by the
combination of H atoms with other elements, can effectively decrease the pressure needed by metallization
of hydrogen [8]. Inspired by this idea, many multihydrogen covalent compounds have been theoretically investigated by structural search method and some of them
have been experimentally realized by means of diamond
anvil cell (DAC) equipment under ultrahigh pressure in
only several advanced laboratory [9]. The sulfur hydride,
(H2 S)2 H2 with Im-3m structure, has been predicted with
favorable Tc of 191-204 K at 200 GPa [10], which was realized in experiment soon afterwards [11]. Stimulated
by high Tc of (H2 S)2 H2 , numerous multi-hydrogen compounds, consisting of H atom and heavy element, have
been explored. For instance, the measured superconductivity of YH9 [12], LaH10 [13, 14] and CaH6 [15] exhibits
Tc of 243, 250-260 and 215 K with the help of DAC equipment, respectively, in which the LaH10 has the highest
critical temperature to date. It is interesting that thorium hydrides has complex superconductivity induced by
their different structures. The measured superconductivity Tc of Th4 H15 [16] and ThH10 [17] is 8.05-8.35 and
161 K at ambient pressure and under 175 GPa, respectively. Moreover, Yu et al. reported that calculated superconductivity Tc of CrH and CrH3 is about 10.60 and
37.10 K under atmospheric pressure and 81 GPa, respectively [18]. The predicted Tc of PdCuH2 is about 34 K
at ambient pressure [19].
As suggested by Ashcroft, the combination of hydrogen with group IVa elements can yield precompression,
2
in which the transformation from insulating to metallic
phases may occur when exerting highly external pressure [8]. The phase transition and electronic property of
carbon hydrides have been investigated by several groups
under high pressure [20–23], however, the superconductivity has not been found until now. The predicted critical temperature of SiH4 featured with wide range can
reach 48-55 [24], 20-75 [25], 16 [26] and 106 K [27] at
90-125, 70-250, 220 and 610 GPa, respectively. The superconductivity of germanium and tin hydrides has been
also explored by several previous investigations [28–33].
It is interesting that, among group-IVa hydrides, the
combination of one of the heaviest element Pb with the
lightest atom H with atomic mass ratio Pb:H=207:1 may
yield favorable superconductivity due to the superconducting property of lead [34]. Cheng et al. theoretically
reported that the metastable PbH4 (H2 )2 can maintain
thermodynamic and dynamic stability above 133 GPa,
in which the predicated maximum of critical temperature can reach 107 K under 230 GPa [35]. Chen et
al. combined crystal structure predictions and electronphonon coupling (EPC) calculations for lead hydrides
and reported two stable compounds under 200 GPa [36].
The PbH6 with C2221 symmetry and PbH8 described by
F ddd symmetry have Tc of 93.33-102.94 K at 100 GPa
and 161.59-178.04 K at 200 GPa, respectively. It can be
seen that the lead hydrides do not form stable plumbane
molecules, which is in contrast to previous lighter groupIVa hydrides, i.e., XH4 (X = C, Si, Ge and Sn). There
is therefore no investigation on superconductivity of fewhydrogen lead hydrides at ambient pressure.
Here, we perform a systematically theoretical study
on the combination of the heaviest element Pb with H
atom, aiming to form stable binary metal-bonded perovskite Pb4 H at ambient pressure, where the H atom, occupied the body-centered site of face-centered cubic (fcc)
Pb atom lattice. This construction is a complete reversal
of the previous multi-hydrogen high-Tc superconductors
under ultrahigh pressure. The structural stability, electronic property, phonon spectrum, electron-phonon coupling and superconductivity of Pb4 H have been comprehensively investigated by means of first-principles calculations and Migdal-Eliashberg theory. We find that the
Pb4 H has excellent superconductivity and ductility at
ambient pressure, providing guidance for further experimental synthesis and motivating more exploration on the
searching potential high-Tc superconductors in the fewhydrogen hydrides under ambient pressure.
II.
COMPUTATIONAL METHODS
The structure optimization and electronic property of
perovskite Pb4 H are calculated based on density functional theory (DFT) as implemented in QUANTUM
ESPRESSO (QE) package [37–39]. The phonon property is investigated by using density functional perturbation theory (DFPT) [40]. The electron-phonon coupling
and superconducting property are studied by using Wannier interpolation [41, 42] and solving Migdal-Eliashberg
equations [43] as integrated in EPW code [44]. The detailed theory and parameters can be found in Supplemental Material.
III.
RESULTS
Considering that the most stable structure of lead is a
fcc lattice with unoccupied body-centered site naturally,
which can be easily occupied by hydrogen because of its
the smallest radius, thus forming binary metal-bonded
perovskite Pb4 H. From the perspective of typical perovskite represented by CaTiO3 , the body-centered interstice can be regarded as a normal lattice point, providing
a chemical precompression for H atom maintaining structural stability without any external pressure. Obviously,
this design strategy is complete reversal of the current design idea of multi-hydrogen high-Tc superconductors under ultrahigh pressure realized by DAC, which presents
potential application capability at ambient pressure. The
crystal structure of perovskite Pb4 H with space group
P m-3m (No. 221) is depicted in Fig. 1 (a), and the corresponding first Brillouin zone and simulated XRD pattern by using VESTA code are presented in Fig. S2 (a)
and (b) of Supplementary Material, respectively. Table I
lists the relaxed lattice constants, atomic distance, conventional cell volume and Wyckoff position together with
Bader charge of Pb4 H. Compared with lead, the lattice
constant of Pb4 H has only a small increase from 4.93 to
4.99, revealing a small lattice expansion.
Let us now assess the structural stability of Pb4 H because this is the precondition of its superconductivity.
Hence, we confirm its stability from structural characteristic, electrostatic potential and phonon dispersion comprehensively. Firstly, from the structural point of view,
the most stable structure of metal lead has a fcc lattice
with the “sphere interstice”, which can be easily occupied by H atom due to its the smallest radius. The stability of hydrogen is maintained without any extrinsic
pressure because of the stable fcc skeleton of lead lattice.
Secondly, we calculate the electrostatic potential on the
Pb-H plane in Pb4 H as illustrated in Fig. 1 (b). It can
be seen that all the Pb and H atoms stand stably at the
bottom of their potential well, guaranteeing their stability. Finally, we further calculate the phonon spectra of
perovskite Pb4 H to verify its dynamic stability, and the
results are presented in Fig. 3 (a) and Fig. S1 (b) of Supplementary Material. It is clear that the imaginary frequency phonon modes are not observed, indicating that
the Pb4 H is dynamically stable. It is well-known that
the fcc lead naturally possesses two competitive interstitial positions, i.e., octahedral (Oh ) and tetrahedral (Td )
sites. We also investigate the structural stability of Pb4 H
with H atom occupied at Td site. We find from Fig. S3
of Supplementary Material that the obviously imaginary
phonon frequencies can be observed, demonstrating its
3
TABLE I. The calculated lattice constant a=b=c, atomic distance Pb(face center) -H(body center) (Pb(vertex) -H(body center) ) between
the body-centered H atom and face-centered (vertex) Pb atom, Wyckoff position, Bader charge and the conventional-cell volume
of perovskite Pb4 H. The corresponding results of fcc lead are also given.
Material
a (Å)
Atomic distance (Å)
Atom
Pb(face center) -H(body center) 2.49 Pb (vertex)
Pb4 H (perovskite) 4.99
Pb (fcc)
4.93
H (body center) 1b (1/2, 1/2, 1/2)
Pb(vertex) -H(body
-
center)
3
Wyckoff position Bader charge (e) Volume (Å )
1a (0, 0, 0)
0.07
4.32 Pb (face center) 3c (0, 1/2, 1/2)
Pb
4a (0, 0, 0)
-0.49
124.25
3×0.14
-
119.82
FIG. 1. Crystal structure, electrostatic potential and electron localization function of Pb4 H. (a) The crystal structure of binary
metal-bonded perovskite Pb4 H, where the green and purple balls represent the Pb and H atoms, respectively. It is clear that the
naturally body-centered site, i.e., octahedral interstice Oh , is occupied by the lightest H atom, forming a binary metal-bonded
perovskite. From the viewpoint of typical perovskite represented by CaTiO3 , the body-centered interstice is a normal lattice
point, which can provide a precompression for H atom maintaining structural stability without any external pressure. (b)
Calculated electrostatic potential on the Pb-H plane. We can find that all Pb and H atoms stand stably at the bottom of their
potential wells, guaranteeing the structural stability. (c) Simulated electron localization function on the Pb-H plane. It can be
seen that the bond characteristic between Pb and H atoms is metallic bond obviously, ensuring the favorable ductility of Pb4 H.
dynamical instability.
We further calculate the electron localization function
of perovskite Pb4 H, namely, the normalized electron density, which is used to intuitively reveal the nature of
chemical bonds between H and Pb atoms. As shown in
Fig. 1 (c), it can be seen that the background on Pb-H
plane is filled by conduction electrons with the normalized electron density of 0.25. Both Pb and H ions are
entrapped in the electron sea, revealing a typically metallic bond combination, which is different from the covalent or ionic bond in multi-hydrogen superconductors under high pressure. The delocalized electrons are mainly
contributed by 6s and 6p valence electrons of Pb atom,
clearly. We can conclude that the Pb-H metallic bond
improves structural stability of perovskite Pb4 H and ensures its better ductility than multi-hydrogen, iron-based
and cuprate superconductors.
Figure 2 (a) presents the projected band structure with
orbital-resolved contribution and corresponding total and
projected density of states (DOS) of perovskite Pb4 H, in
which the two bands, labeled as #1 and #2, cross the
Fermi level (EF =0 eV), demonstrating an obvious metal
energy band. The Wannier interpolation bands are presented in Fig. S1 (a) of Supplementary Material. The
band #1, mainly contributed by H 1s and Pb 6p orbitals,
crosses EF along high symmetry point Γ-X-M-Γ and R-
X, which undoubtedly generates a complex Fermi surface
(FS) sheet with orbital-resolved contribution as shown in
top panels of Fig. 2 (b)-(d). The band #2 is mainly derived from the Pb 6s and 6p orbitals, in line with the
FS colored by orbital contribution in bottom panels of
Fig. 2 (b)-(d), presenting three intersection with EF . We
notice that metal Pb also has two bands crossing the EF ,
which generates a two band superconductivity [34]. It
can be deduced that Pb4 H is a two band superconductor with two distinct superconducting gaps as well. We
find from projected DOS that the contribution of H atom
mainly distributes below the Fermi energy, indicating its
electrons localization, as presented by ELF in Fig. 1 (c).
To clarify the strong electron-phonon coupling mechanism between electronic states and phonon modes, we
calculate the phonon dispersion of perovskite Pb4 H along
the high-symmetry path by using DFPT method [40]
and the Wannier interpolation on enoughly dense kpoint and q-point grids, as performed in the EPW
code [41, 42, 44]. Figure 3 (a) shows the phonon spectrum
with the color representing the phonon linewidth, corresponding phonon DOS and Eliashberg spectrum function
α2 F (ω) together with accumulated EPC constant λ. The
phonon linewidth (see Eq. (S2) of Supplemental Material) is mainly derived from EPC matrix elements and
FS nesting function ξ(q) (see Eq. (S3) of Supplemental
4
FIG. 2. Electronic band structure and Fermi surface colored by orbital weight. (a) Projected band structure of Pb4 H and
corresponding total and projected density of states. The Fermi energy is set to zero. The two bands, labeled as #1 and #2,
intersect with Fermi level, indicating a typical metal energy band. The orbital contributions are presented by the size of the
colored circles. The distribution of the orbital property on the Fermi surfaces for (b) H 1s orbital, (c) Pb 6s orbital and (d)
Pb 6p orbital.
FIG. 3. Phonon dispersion and Fermi surface nesting function. (a) Left: Calculated phonon spectra with the normalized phonon
linewidth encoded in color. Right: Projected phonon density of states and Eliashberg spectral function α2 F (ω) together with
integrated electron-phonon coupling strength λ. (b) The Fermi surface nesting function ξ(q) along high symmetry path.
Material), in which the EPC matrix elements are adopted
to reveal the scattering probability amplitude of an electron on FS sheet through a phonon mode labeled wave
vector q [45] and nesting function can be used to describe
the EPC strength partially. From Fig. 3 (a), it can be
seen that there are two parts of phonon modes divided
from the phonon energy about 15 meV because of the
large mass ratio Pb:H=207:1. The cutoff of low phonon
modes with moderate phonon linewidth contributed by
Pb atom vibration is about 12.62 meV, which is slightly
larger than 8.50 meV of bulk Pb [46]. However, the highfrequency branches introduced by H atom vibration exhibit strong electron-phonon interaction described by the
large phonon linewidth, which plays a significant role to
improve the critical temperature.
We further explore the Eliashberg spectral function
α2 F (ω) and accumulated EPC strength λ by using maximally localized Wannier function, as depicted in right
panel of Fig. 3 (a). It can be seen that there are
three major peaks, centered at 6, 9 and 25 meV, in
spectral function α2 F (ω), which are induced by strong
electron-phonon interaction represented by large phonon
linewidth. The integrated EPC constant λ=1.32, contributed by Pb lattice, is slightly smaller than 1.55 of
bulk Pb obtained from tunneling measurement [47] and
very close to 1.41 of bulk Pb obtained by theoretical calculations [46], revealing that the hydrogen implantation
in fcc Pb has negligible effect on electron-phonon interaction dominated by Pb lattice. The accumulated EPC
parameter λ=1.13, derived from H atom, is about 46% of
total λ, indicating a importantly positive contribution to
improve EPC strength. The total λ=2.45 of Pb4 H has an
5
FIG. 4. EPC strength and superconducting property together with quasiparticle density of states of Pb4 H. (a) The fully
k-resolved EPC constant λnk projected on two FS sheets induced by two crossing bands #1 and #2. (b) The normalized
distribution of EPC parameter λnk . (c) The two FS sheets colored by fully k-resolved superconducting gap ∆nk at 20 K. (d)
Calculated distribution of superconducting gaps ∆nk versus temperature, where the green and blue solid lines represent the
gaps described by the maximum normalized quasiparticle density of states. (e) The normalized quasiparticle density of states
from 15 to 45 K.
enhancement of 58% compared with 1.55 of bulk Pb [47],
and is about three times large than 0.75 of MgB2 [43],
due to the large phonon linewidth of the high-frequency
phonon branches introduced by H atom vibration. It is
interesting that the quite large λ=2.45 of Pb4 H is similar
to the 2.29 of LaH10 at 250 GPa [48] and 2.50 of ThH10
at 100 GPa [49], which provides a typical model to investigate strong electron-phonon interaction under ambient
pressure.
To deeply reveal the physical reason of strong electronphonon coupling strength in perovskite Pb4 H, we further
calculate the nesting function ξ(q) along high-symmetry
path Γ-X-M-Γ-R-X by using Eq. (S3) of Supplemental
Material, as shown in Fig. 3 (b). It is worth pointing
out that the largest value of ξ(q) at Γ point does not
possess actual physical mechanism because the entire FS
sheet nests into itself. It can be seen that there are many
sharp peaks along whole high-symmetry direction, which
quantitatively demonstrates the emergence of strong FS
nesting at these directions. Not coincidentally, the regions of soft phonon modes with large phonon linewidth
are in line with the nesting areas, obviously demonstrating that the strong electron-phonon interaction is partially derived from the FS nesting.
To investigate the anisotropy of EPC parameter in
Pb4 H on FS sheets, we conduct the k-resolved EPC
strength λnk according to the formula [43],
λnk =
X
mk0 ,ν
1
ν
δ (mk0 ) gnk,mk
0
ωqv
2
.
(1)
Figure 4 (a) presents that the variational EPC strength
λnk projects on two FS sheets, where the values of λnk on
FS #1 and #2 are 1.79-6.98 and 0.79-5.66, respectively.
The normalized distribution of λnk , as shown in Fig. 4
(b), also has a wide range of 0.77-6.59, which reveals
strong anisotropy inside each single FS sheet. It is clear
6
that the λnk in FS #1 is larger than that in FS #2. More
specifically, the red area in FS #1 presents the largest
EPC strength, due to the H 1s and Pb 6p electrons strong
coupling with phonons (see top panels of Fig. 2 (b) and
(d)). Whereas, the EPC strength λnk described by FS
#2 is mainly derived from Pb 6s and 6p orbitals (see
bottom panels of Fig. 2 (c) and (d)). It can be predicted
that strong anisotropy of EPC strength can enhance the
critical temperature.
The anisotropic superconducting gaps ∆nk , inside each
FS sheet, have also been explored by numerically solving
the anisotropic Migdal-Eliashberg equations [43], where
the semiempirical Coulomb repulsion pseudopotential µ∗
is set to 0.10. Figure 4 (c) shows the two FS sheets embellished with superconducting gap ∆nk at 20 K. The
gaps ∆nk on the FS #1 and #2 have a wide range of
6.30-12.39 and 2.04-9.15 meV, respectively, revealing the
strong anisotropy of ∆nk on each single FS sheet verified
by the obviously vertical energy spreed (see Fig. 4 (d)).
It is clear that the larger intraband gap anisotropy, the
higher the superconducting transition temperature Tc .
We also find that the distribution of superconducting gap
∆nk on FSs is very similar to that of EPC strength λnk ,
demonstrating that perovskite Pb4 H can be considered
as a typically phonon-mediated high-temperature superconductor.
In the followup analysis, we perform the energy distribution of superconducting gaps ∆nk versus temperature,
as shown in Fig. 4 (d), where the two fully anisotropic
superconducting gaps derived from the two FS sheets
also overlap with each other because of the contiguous
distribution of λnk , i.e., λ1k and λ2k , where n is band
index, derived from the two bands crossing the EF , superimpose with each oher. This is different from the
metal Pb featured with a clear separation between two
superconducting gaps [34]. The gaps labeled by green
and blue solid lines are closely related to the superconducting DOS on FS #1 and #2, respectively (see Fig. 4
(e)). The critical temperature can be defined at T=Tc
with ∆nk =0, we thus obtain the Tc of Pb4 H is 46 K,
which is approximately six times as large as that of lead
(7.22 K) [50], twice larger than Nb3 Ge (23 K) [51] and
higher than MgB2 (39 K) [43]. To clarify the importance of anisotropic effect, the temperature dependence
of isotropic superconducting gaps ∆k have been also investigated by solving isotropic Migdal-Eliashberg equations with µ∗ =0.10. As illustrated in Fig. S4 of Supplemental Material, the calculated critical temperature is 38
K. Clearly, there is 21% improvement in anisotropic superconductivity with respect to isotropic superconductivity due to the presence of multiband and anisotropic gaps.
Considering that perovskite Pb4 H has strong electronphonon interaction featured with large EPC strength
λ=2.45, we further study the superconducting transition
temperature Tc by using µ∗ =0.13. Figure S5 of Supplemental Material shows that the calculated Tc reaches 44
K, indicating that Pb4 H is also a high-Tc superconductor.
The quasiparticle density of states (QPDOS) is a crit-
ical parameter because it can be directly observed by
using tunnel-conductance measurement. We thus calculate the normalized QPDOS in the superconducting
state NS (ω) under the several temperatures by using formula [43],
NS (ω)
ω
],
= Re[ p
N (EF )
ω 2 − ∆2 (ω)
(2)
here the N (EF ) is the DOS at Fermi level in the normal state. We can find from Fig. 4 (e) that the normalized QPDOS, describing the excitation energy below the
critical temperature, has two peaks, corresponding two
different energy gap distributions in perovskite Pb4 H.
Obviously, with the increase of temperature, the superconducting gap decreases and vanishes finally in normal
state.
FIG. 5. The specific-heat difference ∆C=Cs -Cn between the
superconducting and normal states versus temperature derived from the second-oder derivative of the free energy in
perovskite Pb4 H. The inset represents the entropy difference
∆S versus temperature.
The specific heat, a critically observable parameter
closely related to the superconductivity, can be adopted
to reveal the lattice vibration and the nature of superconducting property. We thus compute the specific heat
difference between the superconducting and the normal
states versus temperature derived from the second-order
derivative of the free energy in perovskite Pb4 H by using
the Eq. (S5) of Supplementary Material. We find from
Fig. 5 that the specific-heat difference has the anomaly at
the second-order phase transition of Tc =46 K, indicating
the superconducting property of perovskite Pb4 H. Based
on the formula of Rutgers [52],
∆C =
ATc
4πd
dHc (T )
dT
2
,
(3)
where the A, d and Hc (T) represent atomic weight, density and critical magnetic field. It can be concluded that
the largely abrupt jump of specific heat clearly reveals
7
high Tc and large dHc (T)/dT. We further calculate the
entropy difference between superconducting and normal
states with the help of following formula [53],
Z
Tc
∆S =
T
C s (T ) − C n (T )
dT.
T
(4)
The inset of Fig. 5 shows the entropy difference. It is
interesting that the minimum entropy difference, equivalent to the zero-point of the specific-heat difference,
can√be estimated to be T=25 K, which is close to the
Tc / 3 ≈26.56 K, demonstrating that the following equation is still valid in Pb4 H,
Hc (T) = Hc (0)[1 − (T/Tc )2 ].
(5)
The upper critical magnetic field of Pb4 H is estimated to
be 4948.52 Oe, which is about six times larger than that
of bulk Pb (803 Oe) [54] and about twice as large as that
of niobium (2038 Oe) [55].
ple crystal structure and metallic bonds, is a new highTc superconductor presented both better ductility than
widely investigated multi-hydrogen and iron-based together with cuprate superconductors constructed by ionic
and covalent bonds, and high critical temperature up to
46 K, slightly larger than MgB2 . The electron-phonon
coupling strength of Pb4 H has an improvement of 58%
with respect to that of bulk Pb, because of the new highfrequency optical phonon modes introduced by H atom
featured with quite large phonon linewidth. Correspondingly, the critical temperature of Pb4 H is almost six times
as large as that of bulk Pb. Consequently, it is hoped
that our findings will pave a new way not only to design few-hydrogen metal-bonded hydrides with the hightemperature superconductivity and the simple structure
under ambient pressure, but also for stimulating further
experimental realization in the near future.
ACKNOWLEDGMENTS
IV.
CONCLUSION
In summary, exploration of perovskite Pb4 H at ambient pressure reveals stable crystal structure featured with
high critical temperature by means of the first-principles
calculations and Wannier interpolation together with
the Migdal-Eliashberg equations. The stability of Pb4 H
has been carefully confirmed. We have systematically
investigated the electronic property, lattice vibrations,
electron-phonon coupling and superconductivity of perovskite Pb4 H. The perovskite Pb4 H, featured with sim-
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This work was supported by the Beijing Outstanding
Young Scientist Program (BJJWZYJH0120191000103),
the National Natural Science Foundation of China
(12247143, 12104421, 61734001, 11947218 and
61521004), Zhejiang Provincial Natural Science
Foundation of China (LY23A040005), Knowledge
Innovation Program of Wuhan-Shuguang Project
(2022010801020214), and China Postdoctoral Science
Foundation (2022M712965). We used the High Performance Computing Platform of the Center for Life
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