Superconducting high-pressure phases of disilane.
ABSTRACT High-pressure structures of disilane (Si(2)H(6)) are investigated extensively by means of first-principles density functional theory and a random structure-searching method. Three metallic structures with P-1, Pm-3m, and C2/c symmetries are found, which are more stable than those of XY(3)-type candidates under high pressure. Enthalpy calculations suggest a remarkably wide decomposition (Si and H(2)) pressure range below 135 GPa, above which three metallic structures are stable. Perturbative linear-response calculations for Pm-3m disilane at 275 GPa show a large electron-phonon coupling parameter lambda of 1.397 and the resulting superconducting critical temperature beyond the order of 10(2) K.
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ABSTRACT: Two structural transitions in covalent aluminum hydride AlH3 were characterized at high pressure. A metallic phase stable above 100 GPa is found to have a remarkably simple cubic structure with shortest first-neighbor H-H distances ever measured except in H2 molecule. Although the high-pressure phase is predicted to be superconductive, this was not observed experimentally down to 4 K over the pressure range 120-164 GPa. The results indicate that the superconducting behavior may be more complex than anticipated.Physical Review Letters 03/2008; 100(4):045504. · 7.94 Impact Factor
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ABSTRACT: The elastic constants of the icosahedral boron crystals have been studied by the formulation of Born and Huang. First of all, a technique of symmetry decomposition has been developed for general crystals possessing molecular units in order to see the relaxation mechanism by the internal shift. It is proven that if a librational mode is Raman active, which is often the case, the mode is able to relax the external strain considerably. For α boron, when only central forces are assumed, the c44 component completely vanishes. A shear strain ɛ4 induces rotations of icosahedra, which cancel the shear strain completely. This gives a qualitative account for why this crystal is metastable. The rotations of icosahedra frequently happen in order to relax other types of strain too. This rotation-induced relaxation mechanism is looked upon as a special example of the above general property. The cancellation for ɛ4 would remain in boron carbide, if only central forces are assumed, even though additional elements are introduced in the unit cell. In this case, the stability of the crystal has been ascribed to large noncentral forces, which emerge from the covalent bonds of the linear chain in the unit cell. Another way of stabilizing the crystal structure of α boron is suggested: the surface contact of icosahedra, which is realized in the crystal of Β boron. In this family of crystals, the only direction in which a rotational motion is not induced is the z direction. The deformity of the icosahedron, instead, leads to an unexpected effect on the elasticity of boron carbide. The crystal is shown to be less stiff in the c axis than in the ab plane, despite the strongest interatomic forces being oriented parallel to the c axis. The rhombohedral site slightly deviates from the lattice vector, and this geometry gives rise to a great relaxation in the compression along the c axis.Phys. Rev. B. 04/1997; 55(18).
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ABSTRACT: The electronic and lattice dynamical properties of compressed solid SiH4 have been calculated in the pressure range up to 300 GPa with density functional theory. We find two energetically preferred insulating phases with P2(1)/c and Fdd2 symmetries at low pressures. We demonstrate that the Cmca structure having a layered network is the most likely candidate of the metallic phase of SiH4 over a wide pressure range above 60 GPa. The superconducting transition temperature in this layered metallic phase is found to be in the range of 20-75 K.Physical Review Letters 09/2008; 101(7):077002. · 7.94 Impact Factor
Superconducting high-pressure phases of disilane
Xilian Jina, Xing Menga, Zhi Hea, Yanming Maa, Bingbing Liua, Tian Cuia,1, Guangtian Zoua, and Ho-kwang Maoa,b,1
aState Key Laboratory of Superhard Materials, College of Physics, Jilin University, Changchun 130012, China; and
Institution of Washington, Washington, DC 20015
bGeophysical Laboratory, Carnegie
Contributed by Ho-Kwang Mao, April 20, 2010 (sent for review March 11, 2010)
High-pressure structures of disilane (Si2H6) are investigated exten-
sively by means of first-principles density functional theory and a
random structure-searching method. Three metallic structures with
P-1, Pm-3m, and C2∕c symmetries are found, which are more stable
than those of XY3-type candidates under high pressure. Enthalpy
calculations suggest a remarkably wide decomposition (Si and H2)
pressure range below 135 GPa, above which three metallic struc-
tures are stable. Perturbative linear-response calculations for
Pm-3m disilane at 275 GPa show a large electron-phonon coupling
parameter λ of 1.397 and the resulting superconducting critical
temperature beyond the order of 102K.
metallization ∣ new phase ∣ solid disilane
(1) at ambient pressure. Cuprate superconductors have much
higher critical temperatures. The cuprate superconductor discov-
ered has a critical temperature of 93 K (2), and mercury-based
cuprates have critical temperatures in excess of 130 K. Pressure
causes extraordinary changes in materials and modifies their
properties. This often provides a path for synthesis of novel
materials. Applying BCS theory to hypothetic metallic hydrogen,
Ashcroft realized that it is a conventional superconductor
with a very high-Tc(3). A Tcof the order of 102K was further
proposed under very strong compression by quantitative calcula-
tions (4). This value compares favorably with those in cuprate
superconductors. However, hydrogen remains insulating up to
extremely high pressures, at least up to about 342 GPa (5).
It was recently predicted that group IVa hydrides would also
ing metallic at lower pressures due to chemical precompression
and theoretical studies of germane (16) and stannane (17, 18),
have investigated possible metallization and superconducting
phase transitions at high pressures.Indeed, thetheoretical studies
on germane and stannane have predicted very high Tcof 64 K at
sufficiently encouraged us to prompt studies on a wider range of
hydrides to confirm the prediction (6). Disilane containing a large
fraction(3∕4) ofHatomsisalsoanimportant hydrogen-richcom-
pound and leads to interesting properties under high pressure.
Furthermore, it is more readily available for experimental studies
because of the higher boiling and melting points than silane, ger-
mane, and stannane. However, studies on disilane are very scarce.
Here, we have explored the crystal structures of disilane in a
wide pressure range from 50 to 400 GPa, and three favored struc-
tures, i.e., P-1, Pm-3m, and C2∕c, are found above 135 GPa.
Remarkably, the large Tcof 80 K at 200 GPa for P-1 and
139 K at 275 GPa for Pm-3m are predicted by quantitative
calculations. Up to now, the superconductive Tcof 139 K is much
higher than other group IVa hydrides reported and comparable
with those in cuprate superconductors.
t is known that the highest superconductive critical temperature
(Tc) found for a conventional superconductor is 39 K for MgB2
Results and Discussion
The XY4-type hydrides in group IVa, i.e., methane (CH4), silane
(SiH4), germane (GeH4), and stannane (SnH4), have been inves-
tigated extensively to uncover the high-pressure crystal structures
and pressure-induced metallization in recent years, as mentioned
above. Methane, the first candidate explored, is found to have no
clues of metallization up to 400 GPa by both theoretical (26) and
experimental (27) work. The disputed metallization of silane
suggested that it might not metallize until much higher pressure
above 200 GPa (28). A metallic monoclinic structure of germane
above 196 GPa (16) and superconducting crystal structures of
stannane above 96 GPa (18) have been reported recently. Below
these pressures, germane and stannane are unstable with respect
to elemental decompositions. In general, high pressure is needed
to metallize group IVa hydrides, so 50 GPa is selected as a starting
pressure point for investigating the possible superconducting
high-pressure phases of disilane.
We carried out unconstrained searches at fixed pressures in the
range from 50 to 400 GPa using one, two, three, four, and six SiH3
formula units (f.u.) per cell, and found many different relaxed
structures. Fig. 1 shows our calculated enthalpies of the candidate
structures including random-searching and XY3-type ones,
together with the decomposition (2Si þ 3H2) level (red dot line).
At low pressures below about 135 GPa, P21∕c and P-1 are the
most favorable structures with the lowest enthalpies. However,
in the range from 50 to 135 GPa, disilane with these two struc-
tures is unstable and decomposes into a Si and H2mixture.
A strikingly wide decomposition pressure range from 50 to
135 GPa is revealed. The P-1 disilane becomes stable above about
135 GPa, which is obviously energetically favored over the others
until the pressure close to about 275 GPa. In the vicinity of
275 GPa, the Pm-3m disilane has the lowest enthalpies among
these structures, about 4 meV∕disilane lower than the C2∕c
one (see Fig. 1 Inset). Above 300 GPa, the C2∕c disilane is the
most favorable structure and about 9 meV∕disilane lower than
the Pm-3m one (see Inset of Fig. 1). Obviously, the three struc-
tures we suggested, i.e., P-1, Pm-3m, and C2∕c, are the most
favored structures of disilane under high pressures.
The favored structures of disilane obtained in this work are
shown in Fig. 2, and the corresponding parameters at respective
pressures are listed in Table 1. The P-1 phase consists of two f.u.
(i.e., Si4H12) in a triclinic crystal lattice, as shown in Fig. 2A.
There are eight unequivalent atoms in the primitive cell. The
six H and four Si atoms occupy the crystallographic 2i sites.
The calculated lattice parameters of this triclinic phase (shown
in Table 1) suggest a low symmetry (space group P-1) at
175 GPa. The triclinic lattice with space group P1 was identified
by an X-ray diffraction pattern of phase II of AlH3(30) under
high pressures, too. The two minima of Si-H bonds are 1.530
and 1.537 Å at 175 GPa, related to the unequivalent atoms
H1, H6, and Si2 as listed in Table 1. As discussed below, these
shortest bonds contribute the high-frequency vibrational modes
of phonons. The Pm-3m disilane contains one SiH3unit in each
primitive cell as shown in Fig. 2B. There are two unequivalent
atoms in the primitive cell. The H atom occupies the crystallo-
graphic 3d site and Si atom locates at the 1b site. The lattice
Author contributions: T.C. designed research; X.J., X.M., Z.H., Y.M., B.L., T.C., G.Z., and
H.-K.M. performed research; X.J., T.C., and H.-K.M. analyzed data; and X.J., T.C., and
H.-K.M. wrote the paper.
The authors declare no conflict of interest.
1To whom correspondence may be addressed. E-mail: firstname.lastname@example.org or h.mao@
www.pnas.org/cgi/doi/10.1073/pnas.1005242107 PNAS ∣ June 1, 2010 ∣ vol. 107 ∣ no. 22 ∣ 9969–9973
parameters at 275 GPa are shown in Table 1. This structure is
remarkably simple and completely different from the P-1 and
C2∕c phases of disilane. One silicon atom occupies the center
of cubic cell, and three H atoms locate at the centers of edges
of the cubic lattice. This is the well-known Pm-3m ReO3or
UO3type structure. In the lattice of Pm-3m structure, H atoms
are grouped in eight regular triangles in the corners of cube,
which is characterized by the same distances (1.59 Å at
275 GPa) of the shortest H-H and Si-H bonds. The structure
of C2∕c disilane contains four f.u. in a monoclinic crystal lattice,
as shown in Fig. 2C. The corresponding lattice parameters of this
triclinic crystal at 300 GPa are listed in Table 1. There are four
unequivalent atoms, including three H atoms and one Si atom, in
the conventional cell occupying the crystallographic 8f sites,
where the Si atoms have eightfold coordination with the average
Si-H bond length of 1.554 Å.
The mechanical stability of structure provides a useful insight
into the stability of crystals. The strain energy of a crystal must be
positive against any homogeneous elastic deformations, i.e., the
matrix of elastic constants Cijmust be positive definite (31). It
should note that negative values are not prohibited for Cij
(32). To evaluate the mechanical stability of the three phases,
elastic constants have been calculated and listed in Table 2.
Obviously, the elastic constants of the three structures satisfy
the mechanical stability criteria (31, 33), indicating that the three
structures are mechanically stable.
The calculated electronic band structure and projected density
of states (DOS) for P-1 phase at 175 GPa, Pm-3m phase at
275 GPa, and C2∕c phase at 300 GPa reveal that these phases
are metallic. The less dispersed valence and conduction bands
near the Fermi level intensify the large electronic DOS at the
Fermi level, which are 4.02, 5.96, and 2.80 states/spin/Ry/unit cell
(if a unit cell contains a Si2H6f.u.) for P-1, Pm-3m, and C2∕c,
respectively. These high DOS values might favor the supercon-
ducting behavior. The charts of phonon band structure and
the projected DOS of P-1, Pm-3m, and C2∕c phases calculated
at selected pressures are shown in Fig. 3. The absence of imagin-
ary frequency modes indicates that these structures are stable
enthalpies (red dotted line), which are calculated by adopting the Si and H2structures from refs. 19 and 29, respectively. Inset: Enthalpies in the pressure range
from 250 GPa to 400 GPa.
Main figure: Calculated enthalpies per Si2H6unit of various disilane structures as functions of pressure with respect to the decomposition (2Si þ 3H2)
175 GPa, (B) Pm-3m phase at 275 GPa, and (C) C2∕c phase at 300 GPa. Large
and small atoms are Si and H, respectively.
The structures of disilane under high pressures. (A) The P-1 phase at
Table 1. Details of the favored structures suggested in this work
(Å, deg.)Atomic coordinates (fractional)
a ¼ 3.150 Å
b ¼ 4.398 Å
c ¼ 4.278 Å
α ¼ 73.431°
β ¼ 80.343°
γ ¼ 69.073°
Pm-3ma ¼ 2.249 Å
C2∕ca ¼ 5.081 Å
b ¼ 3.750 Å
c ¼ 5.489 Å
β ¼ 121.925°
The parameters of P-1, Pm-3m, and C2∕c structures correspond to 175, 275
and 300 GPa, respectively.
www.pnas.org/cgi/doi/10.1073/pnas.1005242107 Jin et al.
dynamically. A direct result from PVDOS of these three struc-
tures shows that the heavier Si atoms dominate the low-frequency
vibrations, and the lighter H atoms contribute significantly to the
high-frequency modes, as expected. Remarkably, the two
branches of high-frequency modes, about 70 THz for P-1 disilane,
are mainly due to the two minimum Si-H bond stretching
vibrations (Fig. 3A). In the C2∕c disilane, the variety of Si-H
bond lengths contribute nearly continuous phonon frequencies
by Si-H/Si-H-Sibond stretching/bending vibrations
24 THz (Fig. 3C).
The analyses of lattice dynamic calculations at the zone-center
(Γ point) phonons are useful for further high-pressure experi-
by the irreducible representations of the point group CiðP-1Þ,
OhðPm-3mÞ, and C2hðC2∕cÞ. The optical modes can be analyzed
bythegrouptheory.InP-1phase,Γoptic¼ 21Auþ 24Ag,wherethe
Aumodes are IR active and Agmodes are Raman active. For the
Pm-3m phase, Γoptic¼ 6T1uþ 3T2u, thereinto, the T1umodes are
IR active and T2umodes are silent. In the crystal of C2∕c,
Γoptic¼ 11Auþ 10Buþ 12Agþ 12Bg, where the Au, Bumodes
are IR active and the Ag, Bgare Raman active. The details of
the calculated IR/Raman active frequencies are listed in Table 3.
To explore the superconductivity of these three phases we
suggested, the EPC parameter λ, the logarithmic average phonon
frequency (ωlog), and the Eliashberg phonon spectral function
α2FðωÞ have been investigated at high pressures. The resulting
λ for P-1 phase at 175, 200 GPa and Pm-3m phase at 275 GPa
are 0.980, 1.089, and 1.397, respectively, indicating that the
EPC is fairly strong. The calculated λ for C2∕c phase at
300 GPa is 0.812, a little lower than the other ones. The theore-
tical spectral function α2FðωÞ and the integrated λðωÞ as a func-
tion of frequency at selected pressures are shown in Fig. 4.
The superconducting critical temperature can be estimated from
the Allen–Dynes modified McMillan equation (34) Tc¼ωlog
for many materials with λ < 1.5. The ωlogis calculated directly
from the phonon spectrum. The Coulomb pseudopotential μ?
is often taken as 0.1 for most metals, an appropriate one
proposed by Ashcroft is 0.13 for hydrogen dominant metallic
alloys that has been adopted in the works of GeH4and SnH4
(16, 17). For P-1 phase at 175 and 200 GPa, the calculated
ωlogare 1121.42 K and 1164.28 K. Using μ?of 0.1 and 0.13,
the estimated Tcare 75.63, 64.62 K at 175 GPa, and 91.78,
80.10 K at 200 GPa, respectively. The calculated ωlog of
Pm-3m at 275 GPa and C2∕c at 300 GPa are 1443.60 and
866.13 K, respectively. Using μ?of 0.1 and 0.13, the estimated
Tcare 153.44, 138.86 K for Pm-3m phase and 41.83, 33.97 K
for C2∕c phase, respectively. Remarkably, the estimated Tcof
Pm-3m phase reaches a very high value, i.e., a Tcbeyond the
order of 102K. These current studies inevitably stimulate the
future high-pressure experiments on the structural and conduc-
λ−μ?ð1þ0.62λÞ?, which has been found to be highly accurate
We have used a random structure-searching method to explore
the crystal structures of disilane in a wide pressure range from
50 to 400 GPa. Three metallic structures, i.e., P-1, Pm-3m,
and C2∕c are found and energetically much superior to those
of XY3-type candidates under high pressure. We have revealed
a wide decomposition pressure range from 50 to 135 GPa, above
which these three structures are thermodynamically, mechani-
cally, and dynamically stable. Perturbative linear-response calcu-
lations for the three structures are performed at selected
pressures. Tcof the P-1 phase at 175 and 200 GPa are 65 and
80 K. For C2∕c phase at 300 GPa, the estimated Tcis 34 K.
Remarkably, the estimated Tc of Pm-3m phase at 275 GPa
reaches a very high value of 139 K, a Tcbeyond the order
Table 2. Elastic constants Cij(GPa) of P-1, Pm-3m and C2∕c crystals calculated at 175, 275 and 300 GPa, respectively
939.3 869.9 160.7
1401.6 134.0668.5 1359.6 1427.7
3 598.41634.43 143.60
The phonon band structure and projected phonon DOS charts of (A) P-1 phase at 175 GPa, (B) Pm-3m phase at 275 GPa, and (C) C2∕c phase at 300 GPa,
Jin et al.PNAS
June 1, 2010
We have studied high-pressure phases of Si2H6by means of first-principles
density functional theory (DFT) and the random structure-searching method
(8), which have been used successfully in recent works (19, 20, 21). We design
a set of initial structures by choosing random unit cells, renormalizing the
volume to a reasonable value, and inserting the desired number and types
of atoms at random positions. Each of these structures is then relaxed to a
minimum of the enthalpy at a given pressure. Searches are then repeated for
different numbers of SiH3formula units per cell. Moreover, XY3-type candi-
dates are considered for comparison. A wide variety of XY3-type candidates
have been checked, including X=N, B, Al, Ga, In, Y, Re, Cr, Mn, Fe, Cu, La, Mo,
Ti, Co, Ce, Bi, and Y=H, F, Cl, Br, I, etc. We found three structures (shown in
Fig. 2) that are more stable than the XY3-type candidates energetically.
The underlying ab initio structure relaxations are performed by means of
DFT implemented in the Vienna ab initio simulation package VASP code (22).
For the initial search over structures, the k-point sets are generated sepa-
rately for each unit cell, and no symmetry restrictions are applied. Brillouin
zone (BZ) sampling using a grid of spacing 2π × 0.05 Å−1and a plane-wave
basis set cutoff of 280 eV are found to be sufficient. But we recalculate the
enthalpy curves with higher accuracy using a BZ sampling of 2π × 0.025 Å−1,
a plane-wave basis set with an energy cutoff of 460 eV, and the Perdew–
Burke–Ernzerhof (PBE) generalized gradient approximation (GGA) density
functional (23). The plane-wave pseudopotential method within the
PBE-GGA, through the Quantum-ESPRESSO package (24) is employed to
study the lattice dynamics and electron-phonon coupling (EPC) for P-1,
Pm-3m, and C2∕c structures at selected pressures, where the three structures
are fully reoptimized by VASP calculations. Phonon frequencies are calcu-
lated based on the density functional linear-response method (25). The Mon-
khorst–Pack (MP) grids of 11 × 8 × 8, 16 × 16 × 16, and 10 × 10 × 6 are used for
the three structures accordingly. Subsequently, EPC are calculated in the first
BZ on the same MP q-point meshes using individual EPC matrices obtained
with the 14 × 10 × 10, 18 × 18 × 18, and 14 × 14 × 9 k-point mesh for the three
structures, respectively. All the convergences of the plane-wave basis set and
MP sampling are carefully examined by employing higher kinetic energy
cutoffs and denser grids sets.
ACKNOWLEDGMENTS.We are thankful for financial support from the National
Natural Science Foundation of China (No. 10979001), the National Basic
Research Program of China (No. 2005CB724400), the Cheung Kong Scholars
Program of China, Changjiang Scholar and Innovative Research Team in Uni-
versity (No. IRT0625), and the National Found for Fostering Talents of Basic
Science (No. J0730311). H.K.M. was supported as part of the EFree, an Energy
Frontier Research Center funded by the U.S. Department of Energy, Office of
Science, Office of Basic Energy Sciences under Award Number DE-SC0001057.
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