Crystal Structure and Superconductivity of PH3 at High Pressures

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Crystal Structure and Superconductivity of PH at High Pressures Hanyu Liu, Yinwei Li, Guoying Gao, John S Tse, and Ivan Ivanovich Naumov J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b12009 • Publication Date (Web): 20 Jan 2016 Downloaded from http://pubs.acs.org on January 22, 2016

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The Journal of Physical Chemistry

Crystal Structure and Superconductivity of PH3 at High Pressures Hanyu Liu1,2*, Yinwei Li3, Guoying Gao4, John S. Tse2,5*, Ivan I. Naumov1 1

Geophysical Laboratory, Carnegie Institution of Washington, Washington, DC 20015, USA 2

Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5E2, Canada

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School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou 221116, China 4

State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, China

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

Abstract We have performed a systematic structure search on solid PH3 at high pressures using the particle swarm optimization method. At 100-200 GPa, the search led to two structures which along with others have P-P bonds. These structures are structurally and chemically distinct from those predicted for the high pressure superconducting H2S phase which has a different topology (i.e., does not contain S-S bonds). Phonon and electron-phonon coupling calculations indicate that both structures are dynamically stable and superconducting. The pressure dependence and critical temperature for the monoclinic (C2/m) phase of 83 K at 200 GPa are in excellent agreement with a recent experimental report.

*Corresponding author: [email protected] or [email protected]

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Introduction Theoretical calculations based on the Bardeen-Cooper-Schrieffer (BCS)1 phonon mediated theory of superconductivity indicate that highly compressed solid hydrogen2 and main group hydrogen-rich materials3 can possess high superconducting critical temperatures (Tc) in predicted high-pressure metallic states owing to the high frequency vibrations of the hydrogen component. This proposal has motivated active theoretical and experimental research to search for superconductivity in these hydrogen-containing materials under pressure.4-7 Theoretical calculations based on the BCS theory on a variety of hydrides show the Tc’s indeed are very high.8-13 The predictions contrast with the common view that the BCS-based Tc cannot be much higher than 40 K14. Experimentally, superconductivity had been observed in SiH4 at 120 GPa with a Tc of 17 K6 and in BaReH9, Tc = 7 K above 100 GPa.15 A theoretical calculation predicted that H2S may exhibit superconductivity with a Tc as high as ~80 K above 100 GPa.16 Subsequent experimental electrical conductivity and magnetic measurements of a material formed from compressing H2S showed a Tc of 203 K at 200 GPa17. It was proposed that the superconducting phase is not stoichiometric H2S but likely to be H3S, in which self-consistent harmonic approximation calculations predicted a Tc of 194 K at 200 GPa.18 However, another theoretical study also suggested the formation of a Im-3m (H2S)2(H2)19 structure, with a Tc of 191-204 K at 200 GPa. So far, the exact nature of the superconducting phase of compressed H2S remains elusive. Very recently PH3, an analogue of H2S, was reported to possess high-temperature superconductivity with a Tc of ~100 K at high pressures.20 The study of PH3 may provide an additional example for the understanding of the electron-phonon coupling mechanism responsible for high Tc in compressed H2S and other hydrogen-rich

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materials. In this work, we investigated possible high pressure crystal structures of PH3 using first-principles electronic structure methods. Two possible candidates were found. Furthermore, the calculated Tc’s based on BCS theory on one of the structures agree well with experiment, providing additional support for the proposal that these high critical temperatures can be realized by a phonon-mediated mechanism. Methods The search for low-energy crystalline structures of PH3 at high pressure were performed using particle swarm optimization method implemented in the CALYPSO code.21 This method has been applied successfully in a broad range of crystalline systems ranging from elemental solids to binary and ternary compounds.22-26 Structure searches were performed from 50 to 200 GPa using models consisting of 1-4 formula unit. In general, the search was terminated after the generation of distinct 1500 structures. In additional, we have also performed prediction calculations on PHx (x=1, 2, 4, 5) at 200 GPa. Structural optimizations, enthalpies, electronic structures, and phonons were calculated using the density-functional electronic structure theory (DFT) with the Perdew-Burke-Ernzerhof (PBE)27 generalized gradient approximation. Phonon dispersion and electron-phonon coupling calculations were performed with density functional perturbation theory. Ultrasoft pseudopotentials for P and H were employed with a kinetic energy cutoff of 80 Ry. A q-mesh of 6×6×3 and k-mesh of 24×24×12 for C2/m structure in the first Brillouin zone was used in the electron-phonon coupling (EPC) calculations. The superconductivity calculations were performed with the Quantum-ESPRESSO package.17

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Results and Discussion

Structure prediction calculations were performed at 100, 200 and 250 GPa. From the calculated enthalpies a structure with P212121 symmetry was found to be the most stable phase below 210 GPa but it transforms to a C2/m structure at higher pressures (Fig. 1). Since PH3 has a high concentration of hydrogen, it is important to consider the contribution of the zero point energy (ZPE) to the relative stability of the candidate structures. Using the calculated harmonic frequencies, the inclusion of ZPE energies lowers the transition pressure of P212121 to C2/m significantly, from 210 GPa to 115 GPa. Although both predicted structures contain P-P bonds (Fig. 2), details in the crystal structures are quite different. At 100 GPa, the P-P bond length in the P212121 structure is 2.13 Å. The hydrogen atoms form single P-H bonds in the P-P units and also bridged between neighboring P-P with P-H bond-lengths from 1.38-1.58 Å at 100 GPa. In comparison, in the C2/m structure the P atoms form polymeric chains decorated with P-H bonds. At 200 GPa, the P-P bond-lengths in the chain alternate between 2.06 and 2.09 Å and P-H bond-lengths are 1.41-1.42 Å. At 100 GPa, the ZPEs of P212121 and C2/m are 0.878 eV/f.u. and 0.802 eV/f.u., respectively. In the P212121 structure, the P-H stretch frequencies that contribute most the ZPE are almost 500 cm-1 or 20% higher than C2/m.(Fig. S1) There are additional P-H-P bend modes at 1250-1500 cm-1 in P212121 but absent in C2/m. Notably, both predicted structures are fundamentally different from H3S, the purportedly superconducting phase of compressed H2S at 200 GPa as in the predicted Im-3m H3S

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structure consisted only of S-H bonds and there were no S-S bonds.19 This suggests that the electron-phonon interactions responsible for high Tc superconductivity in PH3 differ from that in H3S.

Fig. 1. Calculated enthalpy of the predicted lowest energy phases of PH3 with and without zero point energy corrections.

Fig. 2. Predicted crystal structures of PH3.The large and small spheres represent the P and H atoms, respectively.

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Fig. 3. Calculated electronic band structures and total density of states (DOS) of (a) P212121 at 100 GPa and (b) C2/m at 200 GPa in PH3. We first analyze the electronic band structures of P212121 and C2/m structured PH3 (Fig. 3). The band dispersions show the metallic behavior of P212121 PH3 at 100 GPa is the result of indirect band overlap. In comparison, the C2/m structure is a genuine metal with parabolic dispersive bands crossing the Fermi level in the A-Γ-Z symmetry axis. Furthermore the electronic bands along L-M-A are also parabolic and cross the Fermi level with steep slopes indicating mobile electrons along these symmetry directions.

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Fig. 4. The phonon spectrum, phonon density of states and Eliashberg phonon spectral function for phase P212121 structure at 100 GPa (a) and C2/m structures at 200 GPa C2/m (b). Red solid circles in (bottom) show the electron-phonon coupling with the radius proportional to their respective strength.

To investigate the superconductive behaviour, phonon and electron-phonon coupling calculations were performed. The phonon band structures reveal no imaginary frequency in P212121 and C2/m structures indicating both are dynamically stable. Phonon band structures and projected density of vibration states within the stable pressure range of these structures are shown in Fig. 4. At 100 GPa (Fig. 4a), the electron-phonon coupling parameter (λ) for the P212121 structure is 0.53 with an average phonon frequency ωln of 990 K defined by the Allen Dynes equation,28 an extension of the McMillan theory for strong coupling.29

Using a nominal Coulomb

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pseudopotential parameter (µ*) of 0.13 the estimated superconducting critical temperature, Tc, is 9 K for the P212121 structure. At 200 GPa, the calculated λ for the C2/m structure of 1.45 is much larger than that of the P212121 phase. With an average phonon frequency ωln of 826 K, again using µ*=0.13, the estimated Tc is 83 K for the C2/m phase.

Fig. 5. The calculated Tc in PH3 along experimental data.20

We investigated the pressure dependence of the critical temperature. The results summarized in Fig. 5 show the Tc for PH3 increases almost linearly with pressure within the range 100 to 200 GPa; a trend in good agreement with experimental data.20 It is clearly seen that calculated Tc of C2/m is better in agreement with experiment results than P212121, suggesting the C2/m phase may be a good candidate of the experimental structure. This finding suggests the calculated Tc for C2/m phase agrees better with the measurements than for P212121 phase and is consistent with the result in Fig. 1 indicating enhanced stability of C2/m phase owing to ZPE. The larger λ and

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higher Tc of the C2/m phase can be traced to the strong Kohn anomalies that considerably soften the P-P phonons along the high symmetry paths (L-M-A-Γ-Z-V).The absence of similar (associated with the S-S bonds) vibrations in H3S means that the particular electron-phonon interactions leading to a relatively high Tc in each case differ, but they still are more effective in H3S. The calculated λ and ωln for the Im-3m structure of H3S are, respectively, 2.19 and 1334 K at 200 GPa.19 These values are to be compared with C2/m PH3 where λ and ωln are 1.46 and 826 K. A smaller λ and ωln in PH3 as compared to H3S leads to a lower Tc in PH3.

Fig. 6. The formation enthalpy of PHx (X=1, 2, 3, 4, 5) at 200 GPa. We also calculated the formation enthalpy of P-H system at high pressures. It is interesting to note that no thermodynamically stable phase relative to elemental P and solid H2 is found until 200 GPa (Fig. 6). The result is similar to a recent preprint arXiv paper on pnictogen hydrides30 but differs from another report.31 In the latter work, the stability of P-H system was investigated systematically and the results suggest PH2 is the most stable phase with a negative formation enthalpy at high

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pressure.31 Furthermore, both enthalpy and superconducting calculations suggest the PH2 may be a possible contestant for the experimentally observed phase.31 A more recent theoretical study32 reported the high pressure phase diagram of PHn (n=1, 2, 3, 4, 5, 6) from structures determined by the Minima Hopping Method.33, 34 The results suggested the lowest energy phases of PH1,2,3 are also superconducting with TC comparable to experiments. In conclusion, theoretical structural search of the crystal structures of PH3 at 100-200 GPa reveal two low energy structures containing P-P bonds. The structures found differ from those predicted for H3S in which contain no heavier element bonds. Electronic band structures and phonon calculations show both the structures are metallic and dynamically stable. Electron-phonon coupling calculations confirm that the C2/m structure is a superconductor with a Tc of 83 K at 200 GPa.

Acknowledgements Work at Carnegie was supported by EFree, an Energy Frontier Research Center funded by the DOE, Office of Science, Basic Energy Sciences under Award No. DE-SC-0001057 (salary support for H.L). The infrastructure and facilities used at Carnegie were supported by NNSA Grant No. DE-NA-0002006, CDAC. A portion of the calculations were performed using computing resources provided by WestGrid, Compute Canada and XSEDE. J.T. and H.L. acknowledge the National Science Foundation of China (11474126) and support from the University of Saskatchewan research computing group and the use of the HPC resources (Plato machine). Y.L acknowledges support from the National Natural Science Foundation of China under Grant Nos. 11204111 and 11404148, the Natural Science Foundation of Jiangsu

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province under Grant No. BK20130223, and the PAPD of Jiangsu Higher Education Institutions.

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Crystal Structure and Superconductivity of PH3 at High Pressures

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