Ion Errea

High-Pressure Hydrogen Sulfide from First Principles: A Strongly Anharmonic Phonon-Mediated Superconductor

We use first-principles calculations to study structural, vibrational, and superconducting properties of H_{2}S at pressures P≥200  GPa. The inclusion of zero-point energy leads to two different possible dissociations of H2S, namely 3H2S→2H3S+S and 5H2S→3H3S+HS2, where both H3S and HS2 are metallic. For H3S, we perform nonperturbative calculations of anharmonic effects within the self-consistent harmonic approximation and show that the harmonic approximation strongly overestimates the electron-phonon interaction (λ≈2.64 at 200 GPa) and Tc. Anharmonicity hardens H─S bond-stretching modes and softens H─S bond-bending modes. As a result, the electron-phonon coupling is suppressed by 30% (λ≈1.84 at 200 GPa). Moreover, while at the harmonic level Tc decreases with increasing pressure, the inclusion of anharmonicity leads to a Tc that is almost independent of pressure. High-pressure hydrogen sulfide is a strongly anharmonic superconductor.

Quantum hydrogen-bond symmetrization in the superconducting hydrogen sulfide system.

Ion Errea1,2,∗ Matteo Calandra3,† Chris J. Pickard, Joseph Nelson, Richard J. Needs, Yinwei Li, Hanyu Liu, Yunwei Zhang, Yanming Ma, and Francesco Mauri3,9‡ Fisika Aplikatua 1 Saila, EUITI Bilbao, University of the Basque Country (UPV/EHU), Rafael Moreno “Pitxitxi” Pasealekua 3, 48013 Bilbao, Basque Country, Spain Donostia International Physics Center (DIPC), Manuel Lardizabal pasealekua 4, 20018 Donostia/San Sebastián, Basque Country, Spain IMPMC, UMR CNRS 7590, Sorbonne Universités UPMC Univ. Paris 06, MNHN, IRD, 4 Place Jussieu, F-75005 Paris, France 4 Department of Materials Science & Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, UK Theory of Condensed Matter Group, Cavendish Laboratory, J J Thomson Avenue, Cambridge CB3 0HE, UK School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou 221116, People’s Republic of China 7 Geophysical Laboratory, Carnegie Institution of Washington, Washington D.C. 20015, USA State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012, People’s Republic of China and 9 Dipartimento di Fisica, Università di Roma La Sapienza, Piazzale Aldo Moro 5, I-00185 Roma, ItalyThe quantum nature of the proton can crucially affect the structural and physical properties of hydrogen compounds. For example, in the high-pressure phases of H2O, quantum proton fluctuations lead to symmetrization of the hydrogen bond and reduce the boundary between asymmetric and symmetric structures in the phase diagram by 30 gigapascals (ref. 3). Here we show that an analogous quantum symmetrization occurs in the recently discovered sulfur hydride superconductor with a superconducting transition temperature Tc of 203 kelvin at 155 gigapascals—the highest Tc reported for any superconductor so far. Superconductivity occurs via the formation of a compound with chemical formula H3S (sulfur trihydride) with sulfur atoms arranged on a body-centred cubic lattice. If the hydrogen atoms are treated as classical particles, then for pressures greater than about 175 gigapascals they are predicted to sit exactly halfway between two sulfur atoms in a structure with symmetry. At lower pressures, the hydrogen atoms move to an off-centre position, forming a short H–S covalent bond and a longer H···S hydrogen bond in a structure with R3m symmetry. X-ray diffraction experiments confirm the H3S stoichiometry and the sulfur lattice sites, but were unable to discriminate between the two phases. Ab initio density-functional-theory calculations show that quantum nuclear motion lowers the symmetrization pressure by 72 gigapascals for H3S and by 60 gigapascals for D3S. Consequently, we predict that the phase dominates the pressure range within which the high Tc was measured. The observed pressure dependence of Tc is accurately reproduced in our calculations for the phase, but not for the R3m phase. Therefore, the quantum nature of the proton fundamentally changes the superconducting phase diagram of H3S.

Anharmonic free energies and phonon dispersions from the stochastic self-consistent harmonic approximation: Application to platinum and palladium hydrides

Harmonic calculations based on density-functional theory are generally the method of choice for the description of phonon spectra of metals and insulators. The inclusion of anharmonic effects is, however, delicate as it relies on perturbation theory requiring a considerable amount of computer time, fast increasing with the cell size. Furthermore, perturbation theory breaks down when the harmonic solution is dynamically unstable or the anharmonic correction of the phonon energies is larger than the harmonic frequencies themselves.We present a stochastic implementation of the self-consistent harmonic approximation valid to treat anharmonicity at any temperature in the non-perturbative regime. The method is based on the minimization of the free energy with respect to a trial density matrix described by an arbitrary harmonic Hamiltonian. The minimization is performed with respect to all the free parameters in the trial harmonic Hamiltonian, namely, equilibrium positions, phonon frequencies and polarization vectors. The gradient of the free energy is calculated following a stochastic procedure. The method can be used to calculate thermodynamic properties, dynamical properties and anharmonic corrections to the Eliashberg function of the electron-phonon coupling. The scaling with the system size is greatly improved with respect to perturbation theory. The validity of the method is demonstrated in the strongly anharmonic palladium and platinum hydrides. In both cases we predict a strong anharmonic correction to the harmonic phonon spectra, far beyond the perturbative limit. In palladium hydrides we calculate thermodynamic properties beyond the quasiharmonic approximation, while in PtH we demonstrate that the high superconducting critical temperatures at 100 GPa predicted in previous calculations based on the harmonic approximation are strongly suppressed when anharmonic effects are included.

Exotic behavior and crystal structures of calcium under pressure

Experimental studies established that calcium undergoes several counterintuitive transitions under pressure: fcc → bcc → simple cubic → Ca-IV → Ca-V, and becomes a good superconductor in the simple cubic and higher-pressure phases. Here, using ab initio evolutionary simulations, we explore the behavior of Ca under pressure and find a number of new phases. Our structural sequence differs from the traditional picture for Ca, but is similar to that for Sr. The β-tin (I41/amd) structure, rather than simple cubic, is predicted to be the theoretical ground state at 0 K and 33–71 GPa. This structure can be represented as a large distortion of the simple cubic structure, just as the higher-pressure phases stable between 71 and 134 GPa. The structure of Ca-V, stable above 134 GPa, is a complex host-guest structure. According to our calculations, the predicted phases are superconductors with Tc increasing under pressure and reaching approximately 20 K at 120 GPa, in good agreement with experiment.

Anharmonic effects in atomic hydrogen: Superconductivity and lattice dynamical stability

We present first-principles calculations of metallic atomic hydrogen in the 400--600 GPa pressure range in a tetragonal structure with space group

Novel superconducting skutterudite-type phosphorus nitride at high pressure from first-principles calculations

I{4}_{1}/amd

Fermi surface nesting and phonon instabilities in simple cubic calcium

, which is predicted to be its first atomic phase. Our calculations show a band structure close to the free-electron-like limit due to the high electronic kinetic energy induced by pressure. Bands are properly described even in the independent electron approximation fully neglecting the electron-electron interaction. Linear-response harmonic calculations show a dynamically stable phonon spectrum with marked Kohn anomalies. Even if the electron-electron interaction has a minor role in the electronic bands, the inclusion of electronic exchange and correlation in the density response is essential to obtain a dynamically stable structure. Anharmonic effects, which are calculated within the stochastic self-consistent harmonic approximation, harden high-energy optical modes and soften transverse acoustic modes up to a 20% in energy. Despite a large impact of anharmonicity has been predicted in several high-pressure hydrides, here the superconducting critical temperature is barely affected by anharmonicity, as it is lowered from its harmonic 318 K value only to 300 K at 500 GPa. We attribute the small impact of anharmonicity on superconductivity to the absence of softened optical modes and the fairly uniform distribution of the electron-phonon coupling among the vibrational modes.

Strong anharmonicity in the phonon spectra of PbTe and SnTe from first principles

State of the art variable composition structure prediction based on density functional theory demonstrates that two new stoichiometries of PN, PN3 and PN2, become viable at high pressure. PN3 has a skutterudite-like Immm structure and is metastable with positive phonon frequencies at pressures between 10 and 100 GPa. PN3 is metallic and is the first reported nitrogen-based skutterudite. Its metallicity arises from nitrogen p-states which delocalise across N4 rings characteristic of skutterudites, and it becomes a good electron-phonon superconductor at 10 GPa, with a Tc of around 18 K. The superconductivity arises from strongly enhanced electron-phonon coupling at lower pressures, originating primarily from soft collective P-N phonon modes. The PN2 phase is an insulator with P2/m symmetry and is stable at pressures in excess of 200 GPa.

Second-order structural phase transitions, free energy curvature, and temperature-dependent anharmonic phonons in the self-consistent harmonic approximation: Theory and stochastic implementation

Phonon instabilities and Fermi surface nesting are studied in the high-pressure simple cubic phase of calcium by means of ab initio calculations. We have focused on nesting along Γ X, which could be responsible for some of the anomalies observed in the phonon spectrum. Phonon frequencies calculated with the density functional perturbation theory are imaginary at several Brillouin-zone points (e.g. at M). However, including anharmonic contributions to the potential might be crucial to stabilize simple cubic calcium, as solving the Schrödinger equation associated to the transversal unstable mode at M gives a positive frequency.

Isotope effect in the superconducting high-pressure simple cubic phase of calcium from first principles

Guilherme A. S. Ribeiro, 2 Lorenzo Paulatto, Raffaello Bianco, 4 Ion Errea, 6 Francesco Mauri, 4 and Matteo Calandra Institut de minéralogie, de physique des matériaux et de cosmochimie (IMPMC), Université Pierre et Marie Curie (Paris VI), CNRS UMR 7590, IRD UMR 206, Case 115, 4 place Jussieu, 75252 Paris Cedex 05, France The Capes Foundation, Ministry of Education of Brazil. Cx. postal 250, Braslia DF 70.040-020, Brazil Dipartimento di Fisica, Università di Roma La Sapienza, Piazzale Aldo Moro 5, I-00185 Roma, Italy Graphene Labs, Fondazione Istituto Italiano di Tecnologia, Via Morego, I-16163 Genova, Italy Fisika Aplikatua 1 Saila, Bilboko Ingeniaritza Eskola, University of the Basque Country (UPV/EHU), Rafael Moreno “Pitxitxi” Pasealekua 3, 48013 Bilbao, Basque Country, Spain Donostia International Physics Center (DIPC), Manuel de Lardizabal pasealekua 4, 20018 Donostia-San Sebastián, Basque Country, Spain (Dated: September 12, 2017)