Two Bounds on the Maximum Phonon-Mediated Superconducting Transition Temperature

Abstract

Two simple bounds on the $T_c$ of conventional, phonon-mediated superconductors are derived within the framework of Eliashberg theory in the strong coupling regime. The first bound is set by the total electron-phonon coupling available within a material given the hypothetical ability to arbitrarily dope the material. This bound is studied by deriving a generalization of the McMillan-Hopfield parameter, $\tilde{\eta }(E)$, which measures the strength of electron-phonon coupling including anisotropy effects and rigid-band doping of the Fermi level to $E$. The second bound is set by the softening of phonons to instability due to strong electron-phonon coupling with electrons at the Fermi level. We apply these bounds to some covalent superconductors including MgB${}_2$, where $T_c$ reaches the first bound, and boron-doped diamond, which is far from its bounds.

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• Superconductivity in diamond
• Properties of the superconducting state in a two-band model
• First-principles Calculation of Superconductivity in Hole-doped LiBC: $T_c=65$ K
• Extreme Electron-Phonon Coupling in Boron-based Layered Superconductors

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