Three-DimensionalMgB2-Type Superconductivity in Hole-Doped Diamond

Abstract

We substantiate by numerical and analytical 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 ${\mathrm{M}\mathrm{g}\mathrm{B}}_2$, albeit in three 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 two to three dimensions reduces the mode softening crucial for $T_c$ reaching 40 K in ${\mathrm{M}\mathrm{g}\mathrm{B}}_2$. Even if diamond had the same bare coupling constant as ${\mathrm{M}\mathrm{g}\mathrm{B}}_2$, which could be achieved with 10% doping, $T_c$ would be only 25 K. Superconductivity above 1 K in Si (Ge) requires hole doping beyond 5% (10%).