Superconductivity of Bi-III phase of elemental bismuth: Insights from muon-spin rotation and density functional theory

Abstract

Using muon-spin rotation the pressure-induced superconductivity in the Bi-III phase of elemental bismuth (transition temperature ${T}_{\mathrm{c}}\ensuremath{\simeq}7.05$ K) was investigated. A Ginzburg-Landau parameter $\ensuremath{\kappa}=\ensuremath{\lambda}/\ensuremath{\xi}=30(6)$ ($\ensuremath{\lambda}$ is the magnetic penetration depth, $\ensuremath{\xi}$ is the coherence length) was estimated, which turns out to be the highest among known single element superconductors. The temperature dependence of the superconducting energy gap $[\mathrm{\ensuremath{\Delta}}(T)]$ reconstructed from ${\ensuremath{\lambda}}^{\ensuremath{-}2}(T)$ deviates from the weakly coupled BCS prediction. The coupling strength $2\mathrm{\ensuremath{\Delta}}/{k}_{\mathrm{B}}{T}_{\mathrm{c}}\ensuremath{\simeq}4.34$ was estimated, thus implying that Bi-III stays within the strong-coupling regime. The density functional theory calculations suggest that superconductivity in Bi-III could be described within the Eliashberg approach with a characteristic phonon frequency ${\ensuremath{\omega}}_{\mathrm{ln}}\ensuremath{\simeq}5.5$ meV. An alternative pairing mechanism to the electron-phonon coupling involves the possibility of Cooper pairing induced by Fermi-surface nesting.