Three-dimensional MgB₂-type superconductivity in hole-doped diamond

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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 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%).