We use first principles calculations to study structural, vibrational and superconducting properties of H2S 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 non-perturbative 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 electronphonon 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.Cuprates [1] have for many years held the world record for the highest superconducting critical temperature (T c = 133 K) [2]. However, despite almost 30 years of intensive research, the physical mechanism responsible for such a high T c is still elusive, although the general consensus is that it is highly non-conventional. The discovery by Drozdov et al.[3] of T c = 190 K in a diamond anvil cell loaded with hydrogen sulfide (H 2 S) and compressed to about 200 GPa breaks the cuprates record and overturns the conventional wisdom that such a high T c cannot be obtained via phonon-mediated pairing.The claim that hydrogen at high pressure could be superconducting is not new [4] and it was recently supported by first principles calculations based on the harmonic approximation applied to dense hydrogen [5][6][7][8] and several hydrides [9][10][11][12][13][14][15]. More recently, two theoretical papers predicted the occurrence of high T c superconductivity in high-pressure sulfur-hydrides [16,17]. However, as shown in Refs. [18,19], anharmonicity can be crucial in these systems. For example, in PdH, the electron-phonon coupling λ parameter is found to be 1.55 at the harmonic level, while a proper inclusion of anharmonic effects leads to λ = 0.40 [18], in better agreement with experiments. Thus, in hydrogen-based compounds, the phonon spectra are strongly affected by anharmonic effects.Several first principles calculations [16,17,20,26] suggested that decomposition of the H 2 S sample occurs within the diamond-anvil cell at high pressures. The high-T c superconducting material is therefore very unlikely to be H 2 S, while H 3 S is the obvious candidate for the H-rich decomposition product.Here we study the structural, vibrational and superconducting properties of H 2 S above 200 GPa, where the highest T c occurs. We show that the inclusion of zero point motion in the convex hull at 200 and 250 GPa stabilizes two metallic structures, H 3 S and HS 2 . Finally, we show that, contrary to suggestions in previous work [16,20], the harmonic approximation does not explain the measured T c ...

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 here 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 even 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.

The 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 Im3m 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 Im3m 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.

Palladium hydrides display the largest isotope effect anomaly known in literature. Replacement of hydrogen with the heavier isotopes leads to higher superconducting temperatures, a behavior inconsistent with harmonic theory. Solving the self-consistent harmonic approximation by a stochastic approach, we obtain the anharmonic free energy, the thermal expansion and the superconducting properties fully ab initio. We find that the phonon spectra are strongly renormalized by anharmonicity far beyond the perturbative regime. Superconductivity is phonon mediated, but the harmonic approximation largely overestimates the superconducting critical temperatures. We explain the inverse isotope effect, obtaining a -0.38 value for the isotope coefficient in good agreement with experiments, hydrogen anharmonicity being the main responsible for the isotope anomaly.PACS numbers: 74.20.Pq,63.20.Ry,74.25.Kc The explanation of the ion-mass isotope effect in phonon-mediated superconductors is one of the greatest success of BCS theory [1]. In a BCS superconductor composed of only one type of ions of mass M , the superconducting critical temperature (T c ) is expected to behave as T c ∝ M −α , where α = 0.5 is the isotope coefficient. In conventional superconductors with more atomic species, the total isotope coefficient should also be close to 0.5. However, in many superconductors like MgB 2 [2], fullerides [3] or high-T c cuprates [4-6] the isotope coefficient is substantially reduced and, in the most extreme case of palladium hydrides (PH), it is even negative [7][8][9].An isotope coefficient α = 0.5 relies on the following assumptions: (i) the phonon frequencies are harmonic, consequently, (ii) the electron-phonon interaction is mass independent, and (iii) the electron-electron interaction is not affected by the isotope substitution. Thus, a reduced isotope effect can either be the fingerprint of a non-conventional mechanism (e.g. spin-fluctuations or correlated superconductivity) or the breakdown of one of these assumptions (e.g. anharmonicity). In both cases, the superconducting state is considered anomalous and current state-of-the-art calculations do not quantitatively account for the behavior of T c as a function of the isotope mass. This is due to the difficulties of dealing either with non-conventional mechanisms or with anharmonicity.Here we consider the most pathological case present in literature, the inverse isotope effect in PH. PdH has T c = 8−9K [7,8]. Hydrogen substitution with the heavier deuterium leads to a higher T c , as T c (PdD) ≈ 10−11K [7,8], leading to α = −[lnT c (PdD) − lnT c (PdH)]/ln2 ≈ −0.3. Remarkably, PdT has a higher T c than PdD, but there is no experimental value at full stoichiometry [9]. A considerable theoretical and experimental effort [10][11][12][13][14][15][16][17][18][19][20][21][22] has been devoted to explain this phenomenon over the last decades. Karakozov et al. [10], in a pioneering work, studied anharmoniciy in PH in the framework of perturbation theory to the bare harmonic phonon...

Pressure‐stabilized hydrides are a new rapidly growing class of high‐temperature superconductors, which is believed to be described within the conventional phonon‐mediated mechanism of coupling. Here, the synthesis of one of the best‐known high‐TC superconductors—yttrium hexahydride Im3¯m‐YH6 is reported, which displays a superconducting transition at ≈224 K at 166 GPa. The extrapolated upper critical magnetic field Bc2(0) of YH6 is surprisingly high: 116–158 T, which is 2–2.5 times larger than the calculated value. A pronounced shift of TC in yttrium deuteride YD6 with the isotope coefficient 0.4 supports the phonon‐assisted superconductivity. Current–voltage measurements show that the critical current IC and its density JC may exceed 1.75 A and 3500 A mm−2 at 4 K, respectively, which is higher than that of the commercial superconductors, such as NbTi and YBCO. The results of superconducting density functional theory (SCDFT) and anharmonic calculations, together with anomalously high critical magnetic field, suggest notable departures of the superconducting properties from the conventional Migdal–Eliashberg and Bardeen–Cooper–Schrieffer theories, and presence of an additional mechanism of superconductivity.

The discovery of superconductivity at 200 K in the hydrogen sulfide system at large pressures [1] was a clear demonstration that hydrogen-rich materials can be high-temperature superconductors. The recent synthesis of LaH10 with a superconducting critical temperature (Tc) of 250 K [2, 3] places these materials at the verge of reaching the long-dreamed room-temperature superconductivity.Electrical and x-ray diffraction measurements determined a weakly pressure-dependent Tc for LaH10 between 137 and 218 gigapascals in a structure with a face-centered cubic (fcc) arrangement of La atoms [3]. Here we show that quantum atomic fluctuations stabilize in all this pressure range a high-symmetry F m-3m crystal structure consistent with experiments, which has a colossal electronphonon coupling of λ ∼ 3.5. Even if ab initio classical calculations neglecting quantum atomic vibrations predict this structure to distort below 230 GPa yielding a complex energy landscape with many local minima, the inclusion of quantum effects simplifies the energy landscape evidencing the F m-3m as the true ground state. The agreement between the calculated and experimental Tc values further supports this phase as responsible for the 250 K superconductivity. The relevance of quantum fluctuations in the energy landscape found here questions many of the crystal structure predictions made for hydrides within a classical approach that at the moment guide the experimental quest for room-temperature superconductivity [4][5][6]. Furthermore, quantum effects reveal crucial to sustain solids with extraordinary electron-phonon coupling that may otherwise be unstable [7]. arXiv:1907.11916v1 [cond-mat.supr-con]

The self-consistent harmonic approximation is an effective harmonic theory to calculate the free energy of systems with strongly anharmonic atomic vibrations, and its stochastic implementation has proved to be an efficient method to study, from first-principles, the anharmonic properties of solids. The free energy as a function of average atomic positions (centroids) can be used to study quantum or thermal lattice instability. In particular the centroids are order parameters in secondorder structural phase transitions such as, e.g., charge-density-waves or ferroelectric instabilities. According to Landau's theory, the knowledge of the second derivative of the free energy (i.e. the curvature) with respect to the centroids in a high-symmetry configuration allows the identification of the phase-transition and of the instability modes. In this work we derive the exact analytic formula for the second derivative of the free energy in the self-consistent harmonic approximation for a generic atomic configuration. The analytic derivative is expressed in terms of the atomic displacements and forces in a form that can be evaluated by a stochastic technique using importance sampling. Our approach is particularly suitable for applications based on first-principles density-functional-theory calculations, where the forces on atoms can be obtained with a negligible computational effort compared to total energy determination. Finally we propose a dynamical extension of the theory to calculate spectral properties of strongly anharmonic phonons, as probed by inelastic scattering processes. We illustrate our method with a numerical application on a toy model that mimics the ferroelectric transition in rock-salt crystals such as SnTe or GeTe.

intercalando átomos de sodio en los llamados materiales de van der Waals. El avance se podría aplicar en tecnologías de la información y sensores biológicos de alta sensibilidad. SINC 4/5/2020 10:47 CEST