Origin of Superconductivity in Boron-doped Diamond

Superconductivity of heavily boron-doped diamond having B concentration of 5$\times 10^{21}$ cm$^{-3}$, reported at T$_c$=4 K by Ekimov {\it et} {\it al}.(April, 2004), is investigated exploiting its electronic and vibrational analogies to MgB$_2$. The deformation potential of the hole states arising from the C-C bond stretch mode is 60\% larger than the corresponding quantity in MgB$_2$ that drives its high T$_c$, leading to very large electron-phonon matrix elements. The calculated coupling strength $\lambda \approx$ 0.5 leads to T$_c$ in the 5-10 K range and makes phonon coupling the likely mechanism. Higher doping should increase T$_c$ somewhat, but effects of three dimensionality primarily on the density of states keep doped diamond from having a T$_c$ closer to that of MgB$_2$.