Superconductivity in heavily vacant diamond

Using first principle electronic structure calculations we investigated the role of substitutional doping of B,N,P,Al and vacancies (${\cal V}$) in diamond (X$_{\alpha}$C$_{1-\alpha}$). In the heavy doping regime, at about $\sim 1-6$ doping an impurity band appears in the mid gap. Increasing further the concentration of the impurity substitution fills in the gap of the diamond host. Our first principle calculation indicates that in the case of vacancies, a clear single-band picture can be employed to write down an effective {\em one band} microscopic Hamiltonian, which can be used to further study various many-body and disorder effects in impurity band (super)conductors.