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

Errea, Ion; Rousseau, Bruno; Bergara, Aitor

doi:10.1063/1.4726161

Cited by 6 publications

(11 citation statements)

References 34 publications

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“…Consequently, calculating fourth-order anharmonic coefficients remains a complicated computational problem and these coefficients have been calculated ab initio exclusively for some specific q points in the 1BZ or in very simple crystal structures 6,8,12,42,52,53 . Therefore, the SCHA has been applied calculating explicitly the fourth-order anharmonic coefficients in the whole 1BZ purely ab initio only in the high-pressure simple cubic phase of calcium 12,42 . Moreover, the restriction to fourth-order terms is an approximation that could be inappropriate and should be verified case by case.…”

Section: The Stochastic Implementation Of the Self-consistent Hamentioning

confidence: 99%

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

2014

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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.

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Section: The Stochastic Implementation Of the Self-consistent Hamentioning

confidence: 99%

“…The method is based on a stochastic evaluation of the free energy and its gradient. Thus, the cumbersome evaluation of anharmonic forces 12,42 or mapping the BO energy surface is avoided. The method is named as the stochastic self-consistent harmonic approximation (SSCHA).…”

Section: Introductionmentioning

confidence: 99%

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

2014

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“…Differently from other methods developed to deal with anharmonic effects [27][28][29], our method allows to access directly the anharmonic free energy of the system, with full inclusion of the anharmonic potential terms, and is variational in the free energy with respect to a trial harmonic potential. Moreover, compared to other implementations of the SCHA [30,31], we replace the cumbersome calculation of anharmonic coefficients by the evaluation of atomic forces on supercells with suitably chosen stochastic ionic configurations.The ionic Hamiltonian is H = T + V , where T and V are the kinetic and potential energy operators. In the adiabatic approximation the potential is defined by the Born-Oppenheimer (BO) energy surface.…”

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confidence: 99%

First-Principles Theory of Anharmonicity and the Inverse Isotope Effect in Superconducting Palladium-Hydride Compounds

2013

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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...

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“…This is very remarkable as with the SSCHA we avoid the cumbersome and time-demanding calculation of φ µµµ1µ1 (−q, q, q 1 , −q 1 ) anharmonic coefficients needed in Eq. (12), which are usually calculated taking first-order numerical derivatives of third-order anharmonic terms or second-order numerical derivatives of dynamical matrices calculated in supercells 12,20,29,[31][32][33] . This result also indicates that in the perturbative limit the SSCHA does not include the bubble self-energy.…”

Section: Combining the Sscha With The Perturbative Expansionmentioning

confidence: 99%

First-principles calculations of phonon frequencies, lifetimes, and spectral functions from weak to strong anharmonicity: The example of palladium hydrides

et al. 2015

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The variational stochastic self-consistent harmonic approximation is combined with the calculation of third-order anharmonic coefficients within density-functional perturbation theory and the "2n+1" theorem to calculate anharmonic properties of crystals. It is demonstrated that in the perturbative limit the combination of these two methods yields the perturbative phonon linewidth and frequency shift in a very efficient way, avoiding the explicit calculation of fourth-order anharmonic coefficients. Moreover, it also allows calculating phonon lifetimes and inelastic neutron scattering spectra in solids where the harmonic approximation breaks down and a non-perturbative approach is required to deal with anharmonicity. To validate our approach, we calculate the anharmonic phonon linewidth in the strongly anharmonic palladium hydrides. We show that due to the large anharmonicity of hydrogen optical modes the inelastic neutron scattering spectra are not characterized by a Lorentzian lineshape, but by a complex structure including satellite peaks.

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

Cited by 6 publications

References 34 publications

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

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

First-Principles Theory of Anharmonicity and the Inverse Isotope Effect in Superconducting Palladium-Hydride Compounds

First-principles calculations of phonon frequencies, lifetimes, and spectral functions from weak to strong anharmonicity: The example of palladium hydrides

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