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%).
Categories: cond-mat.supr-con cond-mat.mtrl-sci