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We substantiate by calculations that the recently discoveredsuperconductivity below 4 K in 3% boron-doped diamond is caused byelectron-phonon coupling of the same type as in MgB$_2$, albeit in 3dimensions. Holes at the top of the zone-centered, degenerate $\sigma$-bondingvalence band couple strongly to the optical bond-stretching modes. The increasefrom 2 to 3 dimensions reduces the mode-softening crucial for $T_{c}$ reaching40 K in MgB$_{2}.$ Even if diamond had the same \emph{bare} coupling constantas MgB$_{2},$ which could be achieved with 10% doping, $T_{c}$ would only be 25K. Superconductivity above 1 K in Si (Ge) requires hole-doping beyond 5% (10%).Comment: revised version, accepted by PR

physical review letters

Three-Dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow><mml:mi mathvariant="normal">M</mml:mi><mml:mi mathvariant="normal">g</mml:mi><mml:mi mathvariant="normal">B</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:math>-Type Superconductivity in Hole-Doped Diamond

Three-DimensionalMgB2-Type Superconductivity in Hole-Doped Diamond