Three-dimensional MgB${}_2$-type superconductivity in hole-doped diamond

Abstract

We substantiate by calculations that the recently discovered superconductivity below 4 K in 3% boron-doped diamond is caused by electron-phonon coupling of the same type as in MgB${}_2$, albeit in 3 dimensions. Holes at the top of the zone-centered, degenerate $\sigma$-bonding valence band couple strongly to the optical bond-stretching modes. The increase from 2 to 3 dimensions reduces the mode-softening crucial for $T_c$ reaching 40 K in MgB${}_2.$ Even if diamond had the same \emph{bare} coupling constant as MgB${}_2,$ which could be achieved with 10% doping, $T_c$ would only be 25 K. Superconductivity above 1 K in Si (Ge) requires hole-doping beyond 5% (10%).

revised version, accepted by PRL

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