Three-dimensional MgB$_{2}$-type superconductivity in hole-doped diamond

TL;DR

This paper demonstrates through calculations that hole-doped diamond exhibits MgB$_{2}$-type superconductivity in three dimensions, with potential for higher critical temperatures if doping levels are increased.

Contribution

It reveals that 3D electron-phonon coupling in hole-doped diamond can lead to MgB$_{2}$-like superconductivity, extending understanding beyond the traditional 2D MgB$_{2}$ system.

Findings

Superconductivity in boron-doped diamond is caused by electron-phonon coupling similar to MgB$_{2}$.

Increasing doping levels could raise the critical temperature up to 25 K.

Superconductivity in Si and Ge requires higher hole-doping percentages.

Abstract

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%).