First-principles study of electron-phonon coupling in hole- and electron-doped diamonds in the virtual crystal approximation

The electronic structure, lattice dynamics, and the electron-phonon coupling (EPC) in hole $(p)$-doped and electron $(n)$-doped diamonds have been extensively investigated using ab initio methods with the virtual crystal approximation. The calculations of $p$-doped diamond correctly reproduced all the essential properties of B-doped diamond such as the increase of lattice constant and the redshift of the Raman spectrum with increasing dopant concentration, and the pressure-induced decrease of ${T}_{c}$. The analysis of the spectral function for $p$-type diamond has shown that optical phonon modes dominate the EPC. From the theoretical prediction of $n$-doped diamond, it is indicated that the metallic $n$-doped diamond might be a good superconductor. It is found that the $\ensuremath{\lambda}$ in $n$-doped diamond increases with the dopant concentration, resulting from the softening of optical phonon modes and the increase of density of states at Fermi level. At a doping level $>2%$, the $\ensuremath{\lambda}$ in $n$-doped diamond is higher than that in $p$-doped diamond. Phonon linewidth and frozen phonon calculations in $n$-doped diamond suggested that the longitudinal optical phonon mode contributes mainly to the EPC. The possible mechanism of the predicted superconductivity in $n$-doped diamond has been discussed.