Superconductivity at ∼100 K in denseSiH4ðH2Þ2 predicted by first principlesYinwei Li, Guoying Gao, Yu Xie, Yanming Ma1, Tian Cui, and Guangtian Zou

State Key Lab of Superhard Materials, Jilin University, Changchun 130012, China

Edited by Ho-Kwang Mao, Carnegie Institution of Washington, Washington, DC, and approved July 28, 2010 (received for review May 25, 2010)

Motivated by the potential high-temperature superconductivity inhydrogen-rich materials, the high-pressure structures of SiH4ðH2Þ2in the pressure range 50–300 GPa were extensively explored byusing a genetic algorithm. An intriguing layered orthorhombic(Ccca) structure was revealed to be energetically stable above248 GPa with the inclusion of zero-point energy. The Ccca structureis metallic and composed of hydrogen shared SiH8 dodecahedralayers intercalated by orientationally ordered molecular H2. Appli-cation of the Allen-Dynes modified McMillan equation yieldsremarkably high superconducting temperatures of 98–107 K at250 GPa, among the highest values reported so far for phonon-mediated superconductors. Analysis reveals a unique supercon-ducting mechanism that the direct interactions between H2 andSiH4 molecules at high pressure play the major role in the highsuperconductivity, while the contribution from H2 vibrons is minor.

H2-containing compounds ∣ high-pressure ∣ high-temperaturesuperconductors ∣ metallization

One of the major targets in high-pressure research is to me-talize solid hydrogen on the search for a high-temperature

superconductor. However, the experimental metallization is yetachieved even at the pressures up to ∼300 GPa (1, 2), abovewhich experiment remains a great difficulty. As an alternative,hydrogen-rich group IV hydrides (i.e., CH4, SiH4, GeH4, andSnH4) are extensively explored since their metallization can hap-pen at much lower pressures (3–9) accessible to current experi-ments. Electric resistivity measurement on SiH4 (6) has revealeda relatively low-temperature superconductivity with a transitiontemperature (Tc) of 17 K at 96 GPa and 120 GPa, though debatesremain (10). The low-temperature superconductivity in SiH4 hasthen been confirmed by theory (8), where SiH4 is found to basi-cally remain at its molecular form at 220 GPa with the shortestH-H distance of 1.35 Å (8). However, subsequent theoreticalresearches on GeH4 and SnH4 have predicted much highersuperconductivities with maximal Tc reaching 64 K at 220 GPafor GeH4 (7) and 62 K at 200 GPa for SnH4 (9), respectively.A common feature on the high-pressure structures of GeH4

and SnH4 is the formation of intriguing semimolecular “H2” unitswith H-H lengths of 0.87 Å (220 GPa) and 0.79 Å (120 GPa),respectively. These H2 units have been found to contribute mostlyto the high superconductivities. This fact illustrates the impor-tance of H2 units in the superconductivity and will inevitablymotivate further search of high-temperature superconductorson those H2 units containing materials.

Remarkably, recent experiments have demonstrated that thesehydrogen-rich full-shell group IV hydrides (CH4 and SiH4) canadsorb additional H2 molecules at high pressures forming a seriesof new H2-containing compounds, e.g., CH4ðH2Þ2, ðCH4Þ2H2,CH4ðH2Þ4, CH4H2 (11), and SiH4ðH2Þ2 (12, 13). In a furthersurvey of literatures, H2 was even found to interact with H2O(14, 15), NH3BH3 (16), Ar (17), and Xe (18) at readily accessiblepressures stabilizing at stoichiometric compounds. The explora-tion of high-pressure metallization of these compounds is greatlydesirable in search of high-temperature superconductors sincehere the demanding H2 units automatically apply.

In view of the low metallization pressure observed in SiH4

(5, 6), we have then targeted on the metallization and supercon-ductivity of SiH4ðH2Þ2 by first-principles calculations via geneticalgorithm on crystal structure prediction and linear responsetheory on electron-phonon coupling (EPC) calculations. Wefocus on the high-pressure regime of 50–300 GPa, below whichSiH4ðH2Þ2 is clearly insulating (13). Our calculations have re-vealed the metallization and a remarkable high superconductivityof SiH4ðH2Þ2 at high pressures. The current results have unra-veled a superconducting mechanism which could have importantimplication on other high-pressure H2-containing compounds,e.g., H2O-H2, CH4-H2, NH3BH3-H2, Ar-H2, and Xe-H2.

Results and DiscussionEvolutionary variable-cell structure predictions were performedat 10, 50, 80, 120, 200, 250, and 300 GPa with one to fourSiH4ðH2Þ2 formula units (f.u.) per cell. At 10 GPa, our calcula-tions predict the correct crystal structure of the synthesizedSiH4ðH2Þ2 (12, 13), where SiH4 molecules form a peculiar tetra-gonal or a distorted face-centered cubic lattice with the orienta-tionally disordered H2 molecules occupying the interstitial sites.The validity of our structural model has been supported by theexcellent mutual agreement between theoretical and experimen-tal equation of states, Raman, andX-ray diffraction data (Fig. S1).Above 50 GPa, analysis of the predicted results gives three beststructures at certain pressure regions, triclinic P-1 (2 f:u:∕cell)at 50 and 80 GPa, monoclinic Cc (4 f:u:∕cell) at 120 GPa, andorthorhombic Ccca (4 f:u:∕cell) at 200, 250, and 300 GPa, as de-picted in Fig. 1 and Table S1. All three structures contain SiHx(x ¼ 6, 8) layers intercalated bymolecular H2 layers. The enthalpycurves of the predicted structures together with the low pressuretetragonal (tI18) phase are plotted as a function of pressure inFig. 2A. The P-1 structure (Fig. 1A) is energetically stable between24 and 92 GPa and still an insulator (Fig. S2). Different from thetetrahedral Si-H bonding in SiH4 molecules of tI18 structure atlow pressure, sixfold-coordinated SiH6 octahedra was formedin P-1 structure. This new bonding feature involves three d orbitalsof Si due to the pressure-induced p-d charge transfers. The H2

molecules sit in between SiH6 layers with H-H bond lengths of0.747 and 0.748 Å, slightly longer than that (0.737 Å) in pure solidH2 (19). Total charge density (Fig. 1D) analysis evidences thedomination of van der Waals interactions between SiH4 and H2

molecules.On compression, the P-1 structure transforms to Cc structure

(Fig. 1B) at 92 GPa. The P-1 → Cc transition is accompanied byan increased Si coordination number from six to eight with theformation of hydrogen shared SiH8 dodecahedra. Note also thatthe puckered Si layers in P-1 structure become planar in Cc struc-ture. The H2 molecules distribute in between SiH8 layers in

Author contributions: Y.M. designed research; Y.L., G.G., Y.X., Y.M., T.C., and G.Z.performed research; Y.L., G.G., and Y.M. analyzed data; and Y.L. and Y.M. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1To whom correspondence should be addressed. E-mail: mym@jlu.edu.cn.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1007354107/-/DCSupplemental.

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various orientations with H-H bond lengths of 0.742 and 0.754 Åat 120 GPa. Weakly covalent H1-H2 bonds have been found inthe Cc structure (Fig. 1E), indicating the increased SiH4-H2 in-teractions under pressure. The Cc structure is a very weak metalwith an extremely low density of states (DOS) at Fermi level(0.17 states∕eV∕unit cell) (Fig. S2) and stable up to 180 GPa,above which the Ccca structure (Fig. 1C) takes over. At the Cc →Ccca transition, the H2 orientations become clearly ordered intwo directions without the major modification of SiH8 dodecahe-dra, but the intramolecular H-H bond was significantly stretchedto be 0.843 Å at 200 GPa, much longer than that in pure solidH2 (19). The elongation of H-H bonds might be mainly resultedfrom the continuously increased SiH4-H2 interactions under pres-sure. Indeed, our total charge density (Fig. 1F) analysis at200 GPa has revealed considerably strong covalent bonding char-acteristics between SiH4 and H2 molecules. This fact furtherimplies that SiH4ðH2Þ2 is no longer a van der Waals compound.We then devised the total energy calculations within the Cccastructure by gradually rotating H2 molecules in b-c plane whileremaining the H2 centers unchanged. A pronounced energyvariation of 0.17 eV∕f:u: is found with a 10° rotation of H2. Sucha large energy barrier naturally prevents H2 from the rotation,resulting in an orientationally ordered H2 in SiH4ðH2Þ2.

The decomposition enthalpies into Siþ 4H2 and SiH4 þ 2H2

are examined to check the phase stability of SiH4ðH2Þ2 underpressure (Fig. 2A). It is surprisingly found that the P-1 and Ccstructures are metastable relative to the decomposition andthe Ccca structure only becomes stable above ∼315 GPa. Onekeeps in mind that quantum effects related to hydrogen atomsare very important. Particularly, the hydrogen zero-point (ZP)energy is expected to be large enough to significantly revisethe structural stability as in the cases of solid hydrogen (19)and hydrides (7, 9). We therefore have estimated the ZP energiesof SiH4ðH2Þ2, SiH4, and H2 at 170 and 240 GPa using the quasi-harmonic approximation (20). It turns out that the inclusion ofZP effects does not change the topology of the phase diagram

(a)A B C

Si

H1

H2

Si

H1

H2

Si

H1

H2

D E F

H1

H2

SiSiH1

H2H2

H1H2H2

0

0.52

1.05

1.57

2.09

0

0.68

1.26

1.83

2.41

0

0.52

1.04

1.56

2.08

H1

H1

H1

Fig. 1. High-pressure crystal structures of SiH4ðH2Þ2: (A) P-1, (B) Cc and (C) Ccca. Large spheres represent Si and small spheres labeled by H1 and H2 denoteH atoms in SiH4 and H2 molecules, respectively. (D–F) The total charge density contours in planes containing Si-H2 and H1-H2 bonds in the P-1 (50 GPa),Cc (120 GPa) and Ccca (200 GPa) structures, respectively.

A

B

Fig. 2. Calculated enthalpy curves for various structures relative to our pre-dicted Cc structure as a function of pressure. The decomposition enthalpiesinto Siþ 4H2 and SiH4 þ 2H2 were also plotted. Inset in (A) is the enthalpies ofCcca structure relative to the SiH4 þ 2H2 without (solid) and with (dashed)zero-point energy corrections. (B) The electronic band structure and pro-jected DOS of the Ccca structure at 250 GPa. In the decomposition calcula-tions, structures of Fd-3m (40) at 0–20 GPa, P6∕mmm (41) at 20–40 GPa,P63∕mmc (41) at 40–80 GPa and Fm-3m (42) above 80 GPa for Si, P21c (43)at 0–40 GPa, Fdd2 (8) at 40–60 GPa, I41a (44) at 40–220 GPa and Pbcn (8)at 220–250 GPa and C2∕c (45) above 250 GPa for SiH4, P63m at 0–100 GPaand C2∕c at 100–250 GPa and Cmca (19) above 250 GPa for H2 (19) areadopted.

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but lowers the decomposition pressure of the Ccca structure into∼248 GPa (inset of Fig. 2A). Therefore, the subsequent electro-nic, phonon, and EPC calculations are focused on the Ccca struc-ture at 250 GPa.

We have explored the electronic band structure and projectedDOS for the Ccca structure and found that Ccca structure is agood metal with a large DOS at Fermi level (0.41 states∕eV∕unit cell) at 250 GPa (Fig. 2B). Flat bands along T-Y andR-Z directions and steep bands along Γ-Z and Y-Γ directionsare evidenced and apparently satisfied with the “Flat-Deep” bandscenario for a good superconductor (21). The projected DOSclearly indicates strong hybridizations of Si, H1 (H atom inSiH4) and H2 (H atom in H2) orbitals. This hybridization resultsin a 25 eV broad valence band favorable for a good superconduc-tor, in accordance with the previous predictions for dense hydro-gen alloys (3). The phonon band structure and projected phononDOS of the Ccca structure at 250 GPa are shown in Fig. 3. Theabsence of any imaginary frequency establishes the dynamical sta-bility of the Ccca structure. Here, the low frequency bands below13 THz and high energy bands above 81 THz are dominated by Sivibrations and H2 vibrons, respectively. It is noteworthy thatstrong coupling of Si-H2 (13–31 THz) and H1-H2 (31–81 THz)vibrations is revealed and largely contrasted to the clear separa-tion of frequency regions found in SiH4, GeH4, and SnH4 (7–9).The strong covalent interactions between SiH4 and H2 moleculesare responsible for this phenomenon.

The Eliashberg spectral function α2FðωÞ∕ω and the EPC para-meter λ of the Ccca structure (Fig. 3C) as a function of frequencyat 250 GPa are calculated to explore the possible superconductiv-ity of SiH4ðH2Þ2. The resulting total λ is 1.625 indicating that theEPC is extremely strong. By applying the calculated logarithmicaverage frequencyωlog (871 K) into the Allen andDynesmodifiedMcMillan equation (22) with a typical choice of Coulomb pseu-dopotential μ� as 0.1–0.13 (3), a remarkable large Tc in the rangeof 98–107 K was derived. The current results support the earliertheoretical proposal that hydrogen dominant metallic alloys arehigh-temperature superconductors (3). However, the Tc magni-tude of ∼100 K strikingly achieved for SiH4ðH2Þ2 is among thehighest values for all previously reported hydrides (6, 7, 9). Thisresult invites us to probe the underlying superconducting mechan-ism originated from the additional H2 molecules. We then decom-pose the total λ into several major individual contributions. Thelow frequency Si translational vibrations (below 13 THz) were

found to contribute 33% in total. It is regretful to find that H2

vibrons (>81 THz) contribute only 1% of λ. Instead, a remarkablefeature prompts to us that the H2-SiH4 coupling (13–81 THz)constitutes ∼66% of the total λ. This result highlights the signifi-cant role played by H2 molecules on the superconductivitythrough the strong interactions with SiH4 molecules enhancingthe attractive EPC over the repulsive Coulomb interaction be-tween electrons. This physicalmechanism is apparently contrastedto those in high-pressure GeH4 (7) and SnH4 (9), where the semi-molecular H-H vibrations dominate the superconductivity.

Remarks on the enthalpy results (Fig. 2A) are necessary beforewe turn to the summary. We find that SiH4ðH2Þ2 decomposes intoSiþ 4H2 at 10–60 GPa, and then SiH4 þ 2H2 at 60–248 GPa.However, it is noteworthy that at relatively low temperatures,a large kinetic barrier might exist and prevent SiH4ðH2Þ2 fromdecomposition. Indeed, experiments (12, 13) observe the stabilityof SiH4ðH2Þ2 at least up to 35 GPa. Previous studies on severalhydrogen containing systems have revealed fairly large activationenergies on decomposition, e.g., 79.3–102.2 KJ∕mol for Al-H(23), 71–74 KJ∕mol for Mg-H (24), and 78 KJ∕mol for Pd-Ni-H(25). An accurate evaluation of decomposition kinetic barrier isneeded to give a precise conclusion, but remains a major chal-lenge and beyond the scope of this study. Nevertheless, if thelarge kinetic barrier could efficiently prevent SiH4ðH2Þ2 from de-composition, the compound can follow the transition paths P-1 →Cc → Ccca and the experimental observation of high supercon-ductivity can be significantly lowered to 180 GPa where much lessexperimental effort is requested. By all appearance, the currentprediction of extremely high superconductivity in SiH4ðH2Þ2might be observable in the range of 180–248 GPa accessible tothe current high-pressure experiments.

In summary, a metallic Ccca phase has been predicted forSiH4ðH2Þ2 most stable above 248 GPa by using first-principle cal-culations. EPC calculations and application of the Allen-Dynesmodified McMillan equation at 250 GPa yield remarkably highcritical temperatures of 98–107 K for the Ccca phase, amongthe highest values reported for hydrogen-rich compounds to date.The current results have unraveled a unique superconductingmechanism where the strong interactions between H2 and SiH4

molecules rather than H2 vibrons dominate the superconductivityof SiH4ðH2Þ2. The stability fields of the Ccca structure are withinthe reach of current experimental techniques. Therefore, the pre-dicted high Tc for SiH4ðH2Þ2 will inevitably stimulate extensiveexperiments. Note that other such high-pressure compounds,e.g., H2O-H2, CH4-H2, NH3BH3-H2, Ar-H2, and Xe-H2, allcontain rich H2 molecules. Future theoretical and experimentalexploration on the metallization and superconductivity of thesecompounds at high pressures are highly demanded.

Materials and MethodsEvolutionary search for the high-pressure structures of SiH4ðH2Þ2 was per-formed by a genetic algorithm (26–28), which has been applied successfullyto a number of systems (7, 9, 29–33). In the evolutionary structural predic-tions, the first generation was created randomly. The subsequent generationis produced from 60% of the lowest-enthalpy structures of the precedinggeneration. In addition, the lowest-enthalpy structures always survived intothe next generation. The variation operators used for producing offspringincluded heredity (60%), lattice mutation (20%), and atomic permutation(20%). The underlying ab initio structure relaxation was performed usingdensity-functional theory (34) within projector augmented wave method(35) as implemented in the Vienna Ab-inito Simulation Package code (VASP)(36). The projector augmented wave potentials used here were derived usingthe generalized gradient approximation (37) functional with valence elec-trons of 3s23p2 and 1s1 and cutoff radii of 1.9 and 0.8 a.u. for Si and H, re-spectively, suitable for the high-pressure study. A plane-wave kinetic energycutoff of 1,000 eV and the use of Monkhorst-Pack (MP) k-points meshes of10 × 10 × 8 for the Ccca structure were shown to given excellent convergenceof the total energy. In the geometrical optimization, all forces on atoms wereconverged to less than 0.001 eV∕Å, and the total stress tensor was reduced tothe order of 0.01 GPa. Lattice dynamic and EPC were calculated using the

A

B

C

Fig. 3. Calculated phonon dispersions (A), phonon density of states (PHDOS)(B), and the Eliashberg phonon spectral function α2FðωÞ∕ω and electron-phonon integral λðωÞ (C) for the Ccca structure at 250 GPa.

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plane-wave pseudopotential method and density-functional perturbationtheory, through the Quantum-opEn Source Package for Research in Electro-nic Structure, Simulation, and Optimization (ESPRESSO) package (38). Forcesand stresses for the converged structures are optimized and checked to bewithin the error between the VASP and ESPRESSO code. Troullier-Martinsnorm-conserving scheme (39) was used to generate the pseudopotentialsfor Si and H. A 6 × 6 × 6 q-point mesh in the first Brillouin zone was usedin the EPC calculation. A MP grid of 16 × 16 × 14 was used to ensure k-point

sampling convergence with Gaussians of width 0.03 Ry, which approximatesthe zero-width limits in the calculations of EPC parameter λ.

ACKNOWLEDGMENTS. We thank the following financial support: theNational Natural Science Foundation of China under Grant No. 10874054,the China 973 Program under Grant No. 2005CB724400; and the 2007 CheungKong Scholars Programme of China. G.G. is also grateful to the Project20092004 supported by Graduate Innovation Fund of Jilin University.

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