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Model for the boron-doping dependence of the critical temperature of superconducting boron-doped diamond

We study the concentration dependence of the superconducting critical temperature Tc in a boron-doped diamond. We evaluate the density of states at Fermi level within the dynamical cluster approximation obtaining higher values than from the coherent potential approximation. We discuss the Tc as a function of density of states within the BCS, the McMillan, and the Belitz theory. The simplified Belitz theory gives the best agreement with experimental data. Since the density of states follows a simple power-law for accessible doping concetrations, the present theory offers an analytical formula for Tc(x).