Abstract
Spin-orbit coupling and electron correlation effects from Os 5d electrons on phonon anharmonicity of β−pyrochlore superconductor KOs2O6 are systematically studied by first-principles frozen-phonon calculations. Spin-orbit coupling eliminates double-well potential, weakens imaginary frequency and enhances lattice stability. However, the gotten T2g and A1g asymmetrical modes show that the lattice is still instable. Then, the on-site Coulomb interaction as an important factor is considered, which completes with the spin-orbit coupling and makes greater influence on the anharmonicity. Therefore, KOs2O6 is a strong spin-orbit coupling and electronic correlation superconductor, and the multiple interactions have great effects on the anharmonicity, which may play an important role to the superconductivity of KOs2O6.
Highlights
Superconductivity and anomalous properties of KOs2O6 have been found due to the inherent geometrical frustration of β−pyrochlore lattice,1–6 which has been proved to be a strong coupling superconductor by the measurement of specific heat, thermodynamic and transport properties.7,8 the phonon spectra9 we reported support the strong electronphonon coupling superconducting mechanism, but imaginary frequency phonon9,10 as an important feature brings great difficulties to direct calculation of electron-phonon coupling constant and superconducting transition temperature Tc
The frequencies of phonon modes at Γ point are obtained by Generalized Gradient Approximation (GGA)+spin-orbit coupling (SOC) calculations, which show that the number of imaginary phonons28–30 is reduced from four to two, only including the Eu and T1u modes. Their frequencies, −155cm−1 and −114cm−1, are obviously higher than −262cm−1 and −232cm−1 from the GGA calculations.9. These mean that the imaginary frequency has been weakened in a great extent by SOC
Compared to the general GGA calculations, the results show that SOC can eliminate double-well potential and enhance lattice stability
Summary
Superconductivity and anomalous properties of KOs2O6 have been found due to the inherent geometrical frustration of β−pyrochlore lattice, which has been proved to be a strong coupling superconductor by the measurement of specific heat, thermodynamic and transport properties. the phonon spectra we reported support the strong electronphonon coupling superconducting mechanism, but imaginary frequency phonon as an important feature brings great difficulties to direct calculation of electron-phonon coupling constant and superconducting transition temperature Tc. The phonon spectra we reported support the strong electronphonon coupling superconducting mechanism, but imaginary frequency phonon as an important feature brings great difficulties to direct calculation of electron-phonon coupling constant and superconducting transition temperature Tc. Whereas, the estimated value of Tc by electron calculations is lower than experimental measurement, which indicates that KOs2O6 is a complex coupling mechanism superconductor besides electron-phonon and electron-spin couplings.. In order to find the influence of the SOC and the U of Os 5d electrons on the phonon anharmonicity of KOs2O6, we develop comprehensive frozen-phonon calculations in this paper, aiming at searching for a channel to eliminate imaginary frequency phonon and giving a better understanding of the pairing mechanism The electronic band structure of KOs2O6 around Fermi level is composed of Os 5d and O 2p hybrid electronic states, which has appreciable effects of spin-orbit coupling (SOC) and on-site Coulomb interaction (U) from localized and correlated Os 5d electrons. anharmonicity is found by the experiments of Raman scattering and coherent inelastic neutron scattering, and obtained by first-principles calculations. in order to find the influence of the SOC and the U of Os 5d electrons on the phonon anharmonicity of KOs2O6, we develop comprehensive frozen-phonon calculations in this paper, aiming at searching for a channel to eliminate imaginary frequency phonon and giving a better understanding of the pairing mechanism
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