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Superconductivity in GeH4(H2)2 above 220 GPa high-pressure
Physica B 410 (2013) 90–92
Contents lists available at SciVerse ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Superconductivity in GeH4(H2)2 above 220 GPa high-pressure Guohua Zhong a,n, Chao Zhang b, Guangfen Wu a, Jianjun Song a, Zhuang Liu a, Chunlei Yang a,n a Center for Photovoltaics and Solar Energy, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences and The Chinese University of Hong Kong, Shenzhen 518055, PR China b Department of Physics, Yantai University, Yantai 264003, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 October 2012 Received in revised form 30 October 2012 Accepted 31 October 2012 Available online 15 November 2012
Hydrogen-rich materials have fascinating physical and chemical properties such as various structures and superconductivity under high-pressure. They are believed as an alternative approach to realize the hydrogen superconducting. In the previous report ([17] Zhong et al., J. Phys. Chem. C 116 (2012) 5225), we had presented structural phase-transitions and bonding interaction variations induced by pressure, and predicted a stable and superconductive phase above 220 GPa, P21/c. In this study, we focus on the change of superconducting transition temperature induced by pressure above 220 GPa for GeH4(H2)2. The variations of bond lengths, electronic structures, phonon spectra, and electron–phonon interaction with the increases of pressure are investigated. We find that the superconducting transition temperature monotonously decreases with the increase of pressure from 230 to 350 GPa. The origin is mainly the stiff of phonon frequency induced by pressurization. & 2012 Elsevier B.V. All rights reserved.
Keywords: Superconductivity Hydrides Germane High-pressure Electronic structure First-principles
1. Introduction Since Wigner and Huntington suggested that hydrogen will transform to metal from insulator at sufficiently high pressure in 1935 (Ref. [1]), hydrogen under pressure has attracted much attention from the scientific community. This interest was further fueled by the Ashcroft’s prediction in 1968 (Ref. [2]) that the metallic hydrogen might even be high-temperature superconductor. This suggestion has motivated considerable experimental and theoretical activities. However, hydrogen remains insulating at extremely high pressure, at least up to 320 GPa [3]. Although estimations based on the infrared data [3] revealed that the band gap closure for solid hydrogen should occur at about 450 GPa, the pressure was extremely difficult to be achieved by the diamond– anvil-cell technique. As an alternative, Ashcroft proposed [4] that the hydrogen-rich alloys should transform into metal under the relatively lower pressure by means of chemical precompressions from the comparable weight elements. Therefore, hydrogen-rich systems have been extensively studied, such as CH4, SiH4, and GeH4. Especially for SiH4 and GeH4, metallization and superconductivity have been theoretically predicted at low or moderate pressure [5–15], although the confirmation of stability and superconductivity still requires more future works from both theory and experiment.
n
Corresponding authors. Tel.: þ 86 755 86392132; fax: þ 86 755 86392299. E-mail addresses: [email protected] (G. Zhong), [email protected] (C. Yang).
0921-4526/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2012.10.039
In addition, the H2-containing compounds by way of the hydrogen-rich closed-shell hydrides (such as CH4, SiH4, GeH4, H2O, and NH3BH3) absorbing additional H2 molecules at high pressures have been investigated to understand the superconductivity and seek for novel superconductors. Inspiringly, recent studies have predicted higher superconducting critical temperature (TC) in SiH4(H2)2 and GeH4(H2)2 than those in SiH4 and GeH4, 98–107 K for SiH4(H2)2 [16] and 76–90 K for GeH4(H2)2 [17] at 250 GPa, respectively. Such high TC motivate our stronger interest to research the kind of H2-containing compounds. In particular, the pressure effect of superconductivity is still unclear. Therefore, in this work, we have investigated the variation of TC with the increase of pressure from 220 GPa to 350 GPa for GeH4(H2)2. 2. Details of calculations The structural optimization and the calculation of electronic structures were performed using the Perdew–Burke–Ernzerhof generalized gradient approximation (GGA) [18] density functional theory and projector augmented wave pseudopotentials [19] as implemented in the Vienna ab initio simulation package (VASP) [20]. An energy cutoff of 800 eV was used for the plane wave basis sets, and 16 16 16 Monkhorst–Pack k-point grids was used for Brillouin zone (BZ) sampling of P21/c phase. In the geometrical optimization, all forces on atoms were converged to less than ˚ and the total stress tensor was reduced to the order of 0.001 eV/A, 0.01 GPa. The lattice dynamical and superconducting properties were calculated by the QUANTUMESPRESSO package [21] with a
G. Zhong et al. / Physica B 410 (2013) 90–92
91
cutoff energy of 60 and 450 Ry for wave functions and charge densities, respectively. Troullier–Martins norm-conserving scheme [22] was used to generate the pseudopotentials for Ge and H. 16 16 12 Monkhorst–Pack k-point grids with Gaussian smearing of 0.03 Ry was used for the phonon calculations at 4 4 3 q-point mesh, and double k-point grids was used in the calculation of the electron–phonon interaction matrix element for P21/c phase of GeH4(H2)2.
3. Results and discussion Our previous study has suggested that GeH4(H2)2 shall stabilize at P21/c phase above 220 GPa pressure [17], so we only focus on this one of high-pressure phases in this study. For P21/c phase above 220 GPa, we have considered these pressure points of 230, 250, 270, 290, 310, 330, and 350 GPa. In order to obtain the electron–phonon coupling constant l, we have calculated the phonon frequencies and the Eliashberg spectral function a2F(o). The electron–phonon coupling constant l is obtained from (Eq.1) Z omax FðoÞ l¼2 a2 d o: ð1Þ 0
Fig. 2. Electronic density of states (DOS) change with the increase of pressure.
o
Then, we calculated the superconducting transition temperature TC using the modified McMillan equation (Eq. (2)) by Allen and Dynes [23] olog 1:04ð1 þ lÞ exp , ð2Þ TC ¼ n 1:2 lm ð1 þ 0:62lÞ where olog is the logarithmic average of phonon frequencies and m is the Coulomb pseudopotential representing Coulombic repulsion. With the typical choice of m* as 0.1–0.15, we present the l and TC dependence on pressure in Fig. 1. It is found that both l and TC are monotonously decreased with the increase of pressure. Using m* ¼0.1, we find the TC reaches to 92 K at 230 GPa while the TC is down to 46 K at 350 GPa. The l is also down to 0.78 at 230 GPa from 1.57 at 350 GPa. It is clear that pressure makes a negative effect for superconductivity in GeH4(H2)2. To understand the variation above, we have also calculated the electronic structures and phonon spectra at pressure points selected. As shown in Figs. 2 and 3, we show the pressureinduced changes of electronic density of states (DOS) and phonon frequencies along high-symmetrical k points, respectively. From our results, pressure results in the decrease of electronic density of states at Fermi level (N(EF)), which means that the electronic Cooper pairs contributing to superconductivity decrease. In addition, by increasing pressure, we observe an increase of phonon
Fig. 3. Phonon spectra along high-symmetry k-point in BZ for several selected pressure points.
Fig. 4. Pressure induces the variations of interatomic distances.
Fig. 1. The superconducting transition temperature TC and electron–phonon coupling constant l dependence on the pressure.
frequency. Namely, the increase of pressure results in the stiff of phonon spectrum. Moreover, we examined the change of interatomic distances under high-pressure to understand the variations of N(EF) and phonon frequency. Fig. 4 shows these results. We find that the bond lengths of d2, d3, d4, and d5 decrease with the increase of pressure except for d1 bond. The decrease of interatomic distances results in the strengthening of hydrogen atomic vibrations, namely, phonon frequencies enhance. At the same time, the compression induced by pressure makes the covalent bond
92
G. Zhong et al. / Physica B 410 (2013) 90–92
And the pressurization leads these peaks shift towards to higher frequency in this range of 310–2560 cm 1. Integrating for the whole frequency, we obtain the decreased electron–phonon coupling constant after pressurizing as shown in Fig. 6. The result shows that the origin of the TC decrease is the stiff of phonon after pressurization.
4. Conclusion
Fig. 5. Band structures along high-symmetry k-point in BZ for several selected pressure points.
We have investigated the superconductivity variation above 220 GPa for GeH4(H2)2 in P21/c phase based on the firstprinciples calculations. It is found that the TC is decreased with the increase of pressure. We have analyzed its origin from the variations of interatomic distances, electronic structures, and phonon vibrations. This origin is that the stiff of phonon frequency reduces the electron–phonon coupling interaction under pressurization.
Acknowledgments The work was supported by the National Natural Science Foundation of China (Grant nos. 11274335 and 61274093), the Basic Research Program of Shenzhen (Grant nos. JC201105190880A, JC201105190912A, JC201104220269A, and JC201105190884A), and the National Basic Research Program of China (973 Program) under Grant no. 2012CB933700. The calculations were performed in HPC Lab, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, People’s Republic of China. References
2
Fig. 6. The Eliashberg phonon function a F(o) and the electron–phonon integral l(o). Solid and dotted lines correspond to 250 and 350 GPa, respectively.
interaction strengthen. The calculated band structures of several pressure points shown in Fig. 5 depict that the pressurization not only leads to the shifting of bands from the Fermi level but also results in the broadening of bands. As a result, this broadening slightly reduces the N(EF) in the range of certain pressures. For the variation of TC, which is important, electron or phonon? To analyzing the origin of TC, we reexamine the band structures and the DOS. As shown in Fig. 5, the change of band structure near Fermi level is very small with the increase of pressure, which indicates that the fermiology is not sensitive to pressure. And the DOS shown in Fig. 2 implies a small change of N(EF) with increasing pressure. Thus, these results suggest that the variation of TC does not mainly come from the change of band structures under pressure. Then, in the cases of two pressures of 250 GPa and 350 GPa, we investigate the Eliashberg spectral functions and the integrations of the electron–phonon coupling strength as a function of phonon frequency. The result is shown in Fig. 6. From the Eliashberg spectral functions, the electron– phonon coupling constant is mainly contributed by the phonons with the frequencies about from 310 to 2560 cm 1 which mainly comes from those vibrations formed by d2, d3, d4, and d5 bonds.
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]
[22] [23]
E. Wigner, H.B. Huntington, J. Chem. Phys. 3 (1935) 764. N.W. Ashcroft, Phys. Rev. Lett. 21 (1968) 1748. P. Loubeyre, F. Occelli, R. Letoullec, Nature 416 (2002) 613. N.W. Ashcroft, Phys. Rev. Lett. 92 (2004) 187002. J. Feng, W. Grochala, T. Jaron´, R. Hoffmann, A. Bergara, N.W. Ashcroft, Phys. Rev. Lett. 96 (2006) 017006. C.J. Pickard, R.J. Needs, Phys. Rev. Lett. 97 (2006) 045504. Y. Yao, J.S. Tse, Y. Ma, K. Tanaka, EPL—Europhys. Lett. 78 (2007) 37003. X.J. Chen, J.L. Wang, V.V. Struzhkin, H.K. Mao, R.J. Hemley, H.Q. Lin, Phys. Rev. Lett. 101 (2008) 077002. M. Martinez-Canales, A.R. Oganov, Y. Ma, Y. Yan, A.O. Lyakhov, A. Bergara, Phys. Rev. Lett. 102 (2009) 087005. B.D. Malone, M.L. Cohen, Phys. Rev. B 85 (2012) 024116. M. Martinez-Canales, A. Bergara, J. Feng, W. Grochala, J. Phys. Chem. Solids 67 (2006) 2095. Z. Li, W. Yu, C. Jin, Solid State Commun. 143 (2007) 353. G. Gao, A.R. Oganov, A. Bergara, M. Martinez-Canales, T. Cui, T. Iitaka, Y. Ma, G. Zou, Phys. Rev. Lett. 101 (2008) 107002. C. Zhang, X.J. Chen, Y.L. Li, V.V. Struzhkin, R.J. Hemley, H.K. Mao, R.Q. Zhang, H.Q. Lin, J. Supercond. Novel Magn. 23 (2010) 717. C. Zhang, X.J. Chen, Y.L. Li, V.V. Struzhkin, H.K. Mao, R.Q. Zhang, H.Q. Lin, EPL—Europhys. Lett. 90 (2010) 66006. Y. Li, G. Gao, Y. Xie, Y. Ma, T. Cui, G. Zou, Proc. Natl. Acad. Sci. USA 107 (2010) 15708. G.H. Zhong, C. Zhang, X.J. Chen, Y.L. Li, R.Q. Zhang, H.Q. Lin, J. Phys. Chem. C 116 (2012) 5225. J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758. G. Kresse, J. Furthmuller, Comput. Mater. Sci. 6 (1996) 15. S. Baroni, A. Dal Corso, S. De Gironcoli, P. Giannozzi, C. Cavazzoni, G. Ballabio, S. Scandolo, G. Chiarotti, P. Focher, A. Pasquarello, K. Laasonen, A. Trave, R. Car, N. Marzari, A. Kokalj, /http://www.pwscf.orgS. N. Troullier, J.L. Martins, Phys. Rev. B 43 (1991) 1993. P.B. Allen, R.C. Dynes, Phys. Rev. B 12 (1975) 905.
Contents lists available at SciVerse ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Superconductivity in GeH4(H2)2 above 220 GPa high-pressure Guohua Zhong a,n, Chao Zhang b, Guangfen Wu a, Jianjun Song a, Zhuang Liu a, Chunlei Yang a,n a Center for Photovoltaics and Solar Energy, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences and The Chinese University of Hong Kong, Shenzhen 518055, PR China b Department of Physics, Yantai University, Yantai 264003, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 October 2012 Received in revised form 30 October 2012 Accepted 31 October 2012 Available online 15 November 2012
Hydrogen-rich materials have fascinating physical and chemical properties such as various structures and superconductivity under high-pressure. They are believed as an alternative approach to realize the hydrogen superconducting. In the previous report ([17] Zhong et al., J. Phys. Chem. C 116 (2012) 5225), we had presented structural phase-transitions and bonding interaction variations induced by pressure, and predicted a stable and superconductive phase above 220 GPa, P21/c. In this study, we focus on the change of superconducting transition temperature induced by pressure above 220 GPa for GeH4(H2)2. The variations of bond lengths, electronic structures, phonon spectra, and electron–phonon interaction with the increases of pressure are investigated. We find that the superconducting transition temperature monotonously decreases with the increase of pressure from 230 to 350 GPa. The origin is mainly the stiff of phonon frequency induced by pressurization. & 2012 Elsevier B.V. All rights reserved.
Keywords: Superconductivity Hydrides Germane High-pressure Electronic structure First-principles
1. Introduction Since Wigner and Huntington suggested that hydrogen will transform to metal from insulator at sufficiently high pressure in 1935 (Ref. [1]), hydrogen under pressure has attracted much attention from the scientific community. This interest was further fueled by the Ashcroft’s prediction in 1968 (Ref. [2]) that the metallic hydrogen might even be high-temperature superconductor. This suggestion has motivated considerable experimental and theoretical activities. However, hydrogen remains insulating at extremely high pressure, at least up to 320 GPa [3]. Although estimations based on the infrared data [3] revealed that the band gap closure for solid hydrogen should occur at about 450 GPa, the pressure was extremely difficult to be achieved by the diamond– anvil-cell technique. As an alternative, Ashcroft proposed [4] that the hydrogen-rich alloys should transform into metal under the relatively lower pressure by means of chemical precompressions from the comparable weight elements. Therefore, hydrogen-rich systems have been extensively studied, such as CH4, SiH4, and GeH4. Especially for SiH4 and GeH4, metallization and superconductivity have been theoretically predicted at low or moderate pressure [5–15], although the confirmation of stability and superconductivity still requires more future works from both theory and experiment.
n
Corresponding authors. Tel.: þ 86 755 86392132; fax: þ 86 755 86392299. E-mail addresses: [email protected] (G. Zhong), [email protected] (C. Yang).
0921-4526/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2012.10.039
In addition, the H2-containing compounds by way of the hydrogen-rich closed-shell hydrides (such as CH4, SiH4, GeH4, H2O, and NH3BH3) absorbing additional H2 molecules at high pressures have been investigated to understand the superconductivity and seek for novel superconductors. Inspiringly, recent studies have predicted higher superconducting critical temperature (TC) in SiH4(H2)2 and GeH4(H2)2 than those in SiH4 and GeH4, 98–107 K for SiH4(H2)2 [16] and 76–90 K for GeH4(H2)2 [17] at 250 GPa, respectively. Such high TC motivate our stronger interest to research the kind of H2-containing compounds. In particular, the pressure effect of superconductivity is still unclear. Therefore, in this work, we have investigated the variation of TC with the increase of pressure from 220 GPa to 350 GPa for GeH4(H2)2. 2. Details of calculations The structural optimization and the calculation of electronic structures were performed using the Perdew–Burke–Ernzerhof generalized gradient approximation (GGA) [18] density functional theory and projector augmented wave pseudopotentials [19] as implemented in the Vienna ab initio simulation package (VASP) [20]. An energy cutoff of 800 eV was used for the plane wave basis sets, and 16 16 16 Monkhorst–Pack k-point grids was used for Brillouin zone (BZ) sampling of P21/c phase. In the geometrical optimization, all forces on atoms were converged to less than ˚ and the total stress tensor was reduced to the order of 0.001 eV/A, 0.01 GPa. The lattice dynamical and superconducting properties were calculated by the QUANTUMESPRESSO package [21] with a
G. Zhong et al. / Physica B 410 (2013) 90–92
91
cutoff energy of 60 and 450 Ry for wave functions and charge densities, respectively. Troullier–Martins norm-conserving scheme [22] was used to generate the pseudopotentials for Ge and H. 16 16 12 Monkhorst–Pack k-point grids with Gaussian smearing of 0.03 Ry was used for the phonon calculations at 4 4 3 q-point mesh, and double k-point grids was used in the calculation of the electron–phonon interaction matrix element for P21/c phase of GeH4(H2)2.
3. Results and discussion Our previous study has suggested that GeH4(H2)2 shall stabilize at P21/c phase above 220 GPa pressure [17], so we only focus on this one of high-pressure phases in this study. For P21/c phase above 220 GPa, we have considered these pressure points of 230, 250, 270, 290, 310, 330, and 350 GPa. In order to obtain the electron–phonon coupling constant l, we have calculated the phonon frequencies and the Eliashberg spectral function a2F(o). The electron–phonon coupling constant l is obtained from (Eq.1) Z omax FðoÞ l¼2 a2 d o: ð1Þ 0
Fig. 2. Electronic density of states (DOS) change with the increase of pressure.
o
Then, we calculated the superconducting transition temperature TC using the modified McMillan equation (Eq. (2)) by Allen and Dynes [23] olog 1:04ð1 þ lÞ exp , ð2Þ TC ¼ n 1:2 lm ð1 þ 0:62lÞ where olog is the logarithmic average of phonon frequencies and m is the Coulomb pseudopotential representing Coulombic repulsion. With the typical choice of m* as 0.1–0.15, we present the l and TC dependence on pressure in Fig. 1. It is found that both l and TC are monotonously decreased with the increase of pressure. Using m* ¼0.1, we find the TC reaches to 92 K at 230 GPa while the TC is down to 46 K at 350 GPa. The l is also down to 0.78 at 230 GPa from 1.57 at 350 GPa. It is clear that pressure makes a negative effect for superconductivity in GeH4(H2)2. To understand the variation above, we have also calculated the electronic structures and phonon spectra at pressure points selected. As shown in Figs. 2 and 3, we show the pressureinduced changes of electronic density of states (DOS) and phonon frequencies along high-symmetrical k points, respectively. From our results, pressure results in the decrease of electronic density of states at Fermi level (N(EF)), which means that the electronic Cooper pairs contributing to superconductivity decrease. In addition, by increasing pressure, we observe an increase of phonon
Fig. 3. Phonon spectra along high-symmetry k-point in BZ for several selected pressure points.
Fig. 4. Pressure induces the variations of interatomic distances.
Fig. 1. The superconducting transition temperature TC and electron–phonon coupling constant l dependence on the pressure.
frequency. Namely, the increase of pressure results in the stiff of phonon spectrum. Moreover, we examined the change of interatomic distances under high-pressure to understand the variations of N(EF) and phonon frequency. Fig. 4 shows these results. We find that the bond lengths of d2, d3, d4, and d5 decrease with the increase of pressure except for d1 bond. The decrease of interatomic distances results in the strengthening of hydrogen atomic vibrations, namely, phonon frequencies enhance. At the same time, the compression induced by pressure makes the covalent bond
92
G. Zhong et al. / Physica B 410 (2013) 90–92
And the pressurization leads these peaks shift towards to higher frequency in this range of 310–2560 cm 1. Integrating for the whole frequency, we obtain the decreased electron–phonon coupling constant after pressurizing as shown in Fig. 6. The result shows that the origin of the TC decrease is the stiff of phonon after pressurization.
4. Conclusion
Fig. 5. Band structures along high-symmetry k-point in BZ for several selected pressure points.
We have investigated the superconductivity variation above 220 GPa for GeH4(H2)2 in P21/c phase based on the firstprinciples calculations. It is found that the TC is decreased with the increase of pressure. We have analyzed its origin from the variations of interatomic distances, electronic structures, and phonon vibrations. This origin is that the stiff of phonon frequency reduces the electron–phonon coupling interaction under pressurization.
Acknowledgments The work was supported by the National Natural Science Foundation of China (Grant nos. 11274335 and 61274093), the Basic Research Program of Shenzhen (Grant nos. JC201105190880A, JC201105190912A, JC201104220269A, and JC201105190884A), and the National Basic Research Program of China (973 Program) under Grant no. 2012CB933700. The calculations were performed in HPC Lab, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, People’s Republic of China. References
2
Fig. 6. The Eliashberg phonon function a F(o) and the electron–phonon integral l(o). Solid and dotted lines correspond to 250 and 350 GPa, respectively.
interaction strengthen. The calculated band structures of several pressure points shown in Fig. 5 depict that the pressurization not only leads to the shifting of bands from the Fermi level but also results in the broadening of bands. As a result, this broadening slightly reduces the N(EF) in the range of certain pressures. For the variation of TC, which is important, electron or phonon? To analyzing the origin of TC, we reexamine the band structures and the DOS. As shown in Fig. 5, the change of band structure near Fermi level is very small with the increase of pressure, which indicates that the fermiology is not sensitive to pressure. And the DOS shown in Fig. 2 implies a small change of N(EF) with increasing pressure. Thus, these results suggest that the variation of TC does not mainly come from the change of band structures under pressure. Then, in the cases of two pressures of 250 GPa and 350 GPa, we investigate the Eliashberg spectral functions and the integrations of the electron–phonon coupling strength as a function of phonon frequency. The result is shown in Fig. 6. From the Eliashberg spectral functions, the electron– phonon coupling constant is mainly contributed by the phonons with the frequencies about from 310 to 2560 cm 1 which mainly comes from those vibrations formed by d2, d3, d4, and d5 bonds.
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]
[22] [23]
E. Wigner, H.B. Huntington, J. Chem. Phys. 3 (1935) 764. N.W. Ashcroft, Phys. Rev. Lett. 21 (1968) 1748. P. Loubeyre, F. Occelli, R. Letoullec, Nature 416 (2002) 613. N.W. Ashcroft, Phys. Rev. Lett. 92 (2004) 187002. J. Feng, W. Grochala, T. Jaron´, R. Hoffmann, A. Bergara, N.W. Ashcroft, Phys. Rev. Lett. 96 (2006) 017006. C.J. Pickard, R.J. Needs, Phys. Rev. Lett. 97 (2006) 045504. Y. Yao, J.S. Tse, Y. Ma, K. Tanaka, EPL—Europhys. Lett. 78 (2007) 37003. X.J. Chen, J.L. Wang, V.V. Struzhkin, H.K. Mao, R.J. Hemley, H.Q. Lin, Phys. Rev. Lett. 101 (2008) 077002. M. Martinez-Canales, A.R. Oganov, Y. Ma, Y. Yan, A.O. Lyakhov, A. Bergara, Phys. Rev. Lett. 102 (2009) 087005. B.D. Malone, M.L. Cohen, Phys. Rev. B 85 (2012) 024116. M. Martinez-Canales, A. Bergara, J. Feng, W. Grochala, J. Phys. Chem. Solids 67 (2006) 2095. Z. Li, W. Yu, C. Jin, Solid State Commun. 143 (2007) 353. G. Gao, A.R. Oganov, A. Bergara, M. Martinez-Canales, T. Cui, T. Iitaka, Y. Ma, G. Zou, Phys. Rev. Lett. 101 (2008) 107002. C. Zhang, X.J. Chen, Y.L. Li, V.V. Struzhkin, R.J. Hemley, H.K. Mao, R.Q. Zhang, H.Q. Lin, J. Supercond. Novel Magn. 23 (2010) 717. C. Zhang, X.J. Chen, Y.L. Li, V.V. Struzhkin, H.K. Mao, R.Q. Zhang, H.Q. Lin, EPL—Europhys. Lett. 90 (2010) 66006. Y. Li, G. Gao, Y. Xie, Y. Ma, T. Cui, G. Zou, Proc. Natl. Acad. Sci. USA 107 (2010) 15708. G.H. Zhong, C. Zhang, X.J. Chen, Y.L. Li, R.Q. Zhang, H.Q. Lin, J. Phys. Chem. C 116 (2012) 5225. J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758. G. Kresse, J. Furthmuller, Comput. Mater. Sci. 6 (1996) 15. S. Baroni, A. Dal Corso, S. De Gironcoli, P. Giannozzi, C. Cavazzoni, G. Ballabio, S. Scandolo, G. Chiarotti, P. Focher, A. Pasquarello, K. Laasonen, A. Trave, R. Car, N. Marzari, A. Kokalj, /http://www.pwscf.orgS. N. Troullier, J.L. Martins, Phys. Rev. B 43 (1991) 1993. P.B. Allen, R.C. Dynes, Phys. Rev. B 12 (1975) 905.