Comparison of the pressure dependences of ${T}_{c}$ in the trivalent $d$-electron superconductors Sc, Y, La, and Lu up to megabar pressures

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Comparison of the pressure dependences of $T_{c}$ in the trivalent $d$ -electron superconductors Sc, Y, La, and Lu up to megabar pressures

M. Debessai, J. J. Hamlin, and J. S. Schilling

Phys. Rev. B 78, 064519 – Published 28 August 2008

Abstract

Whereas double hcp (dhcp) La superconducts at ambient pressure with $T_{c} ≃ 5 K$ , the other trivalent $d$ -electron metals Sc, Y, and Lu only superconduct if high pressures are applied. Earlier measurements of the pressure dependence of $T_{c}$ for Sc and Lu metal are here extended to much higher pressures. Whereas $T_{c}$ for Lu increases monotonically with pressure to 12.4 K at 174 GPa (1.74 Mbar), $T_{c}$ for Sc reaches 19.6 K at 107 GPa, the second highest value observed for any elemental superconductor. At higher pressures a phase transition occurs whereupon $T_{c}$ drops to 8.31 K at 111 GPa. The $T_{c} (P)$ dependences for Sc and Lu are compared with those of Y and La. An interesting correlation is pointed out between the value of $T_{c}$ and the fractional free volume available to the conduction electrons outside the ion cores, a quantity which is directly related to the number of $d$ electrons in the conduction band.