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 MgB2, albeit in 3 dimensions. Holes at the top of the zone-centered, degenerate σ-bonding valence band couple strongly to the optical bond-stretching modes. The increase from 2 to 3 dimensions reduces the mode-softening crucial for Tc reaching 40 K in MgB2. Even if diamond had the same \emph{bare} coupling constant as MgB2, which could be achieved with 10% doping, Tc would only be 25 K. Superconductivity above 1 K in Si (Ge) requires hole-doping beyond 5% (10%).
@article{arxiv.cond-mat/0404447,
title = {Three-dimensional MgB$_{2}$-type superconductivity in hole-doped diamond},
author = {Lilia Boeri and Jens Kortus and O. K. Andersen},
journal= {arXiv preprint arXiv:cond-mat/0404447},
year = {2007}
}