Motivated by the discovery of superconductivity in boron-doped (B-doped) diamond, we investigate the localization and superconductivity in heavily doped semiconductors. The competition between Anderson localization and s-wave superconductivity is investigated from the microscopic point of view. The effect of microscopic inhomogeneity and the thermal fluctuation in superconductivity are taken into account using the self-consistent 1-loop-order theory with respect to superconducting fluctuation. The crossover from superconductivity in the host band to that in the impurity band is described on the basis of the disordered three-dimensional attractive Hubbard model for binary alloys. We show that superconductor-insulator transition (SIT) accompanies the crossover. We point out an enhancement of Cooper pairing in the crossover regime. Further localization of the electron wave function gives rise to incoherent Cooper pairs and the pseudogap above Tc. A global phase diagram is drawn for host band superconductivity, impurity band superconductivity, Anderson localization, Fermi liquid state, and pseudogap state. A theoretical interpretation is proposed for superconductivity in the doped diamond, SiC, and Si.

We investigate the localization and superconductivity in heavily doped semiconductors. The crossover from the superconductivity in the host band to that in the impurity band is described on the basis of the disordered three-dimensional attractive Hubbard model for binary alloys. The microscopic inhomogeneity and the thermal superconducting fluctuation are taken into account using the self-consistent 1-loop order theory. The superconductor-insulator transition accompanies the crossover from the host band to the impurity band. We point out an enhancement of the critical temperature T c around the crossover. Further localization of electron wave functions leads to the localization of Cooper pairs and induces the pseudogap. We find that both the doping compensation by additional donors and the carrier increase by additional acceptors suppress the superconductivity. A theoretical interpretation is proposed for the superconductivity in the boron-doped diamond, SiC, and Si.