Strong coupling superconductivity mediated by three-dimensional anharmonic phonons

Abstract

We investigate three dimensional anharmonic phonons in tetrahedral symmetry and superconductivity mediated by these phonons. Three dimensional anharmonic phonon spectra are calculated directly by solving Schrödinger equation and the superconducting transition temperature is determined by using the theory of strong coupling superconductivity assuming an isotropic gap function. With increasing the third order anharmonicity $b$ of the tetrahedral ion potential, we find a crossover in the energy spectrum to a quantum tunneling regime. We obtain strongly enhanced transition temperatures around the crossover point. We also investigate the anharmonic effects on the Debye-Waller factor, the phonon spectral functions and the density profile, as a function of the anharmonicity $b$ and temperature. The isomorphic first order transition observed in KOs_2O_6 is discussed in terms of the first excited state energy $\Delta$, and the coupling constant $\lambda$ in the strong coupling theory of superconductivity. Our results suggest the decrease of $\lambda$ and increase of $\Delta$ below the first order transition temperature. We point out that the change in the oscillation amplitude <x^2> and <xyz> characterizes this isomorphic transition. The chemical trends of the superconducting transition temperature, $\lambda$, and $\Delta$ in the $\beta$-pyrochlore compounds are also discussed.

16 pages, 17 figures, Phys. Rev. B 81, 134503 (2010).

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• Kondo Effect of a Vibrating Magnetic Impurity
• Strong-Coupling Theory of Rattling-Induced Superconductivity
• Anharmonic theory of superconductivity and its applications to emerging quantum materials
• Kondo Effect of a Magnetic Ion Vibrating in a Harmonic Potential
• Phonon Dynamics and Multipolar Isomorphic Transition in beta-pyrochlore KOs2O6
• Heavy-Electron Formation and Bipolaronic Transition in the Anharmonic Holstein Model
• Novel K Rattling: A New Route to Thermoelectric Materials?
• Superconducting and Structural Transitions in the β-Pyrochlore Oxide KOs2O6 under High Pressure
• Physical properties of noncentrosymmetric tungsten and molybdenum aluminides
• Superconductivity and Rattling under High Pressure in the beta-Pyrochlore Oxide RbOs2O6
• Novel Rattling of K Atoms in Aluminium-Doped Defect Pyrochlore Tungstate
• Anomalous Isotope Effect in Rattling-Induced Superconductor
• Towards a Mechanism of Rattler Coupling in the β-Pyrochlores AOs2O6 (A = K, Rb, Cs)