Effect of structural disorder and Coulomb interactions in the superconductor-insulator transition applied to boron doped diamond

The effect of disorder, both structural (non-diagonal) and on-site (diagonal), is studied through the inhomogeneous Bogoliubov-de Gennes (BdG) theory in narrow-band disordered superconductors with a view towards understanding superconductivity in boron doped diamond (BDD) and boron-doped nanocrystalline diamond (BNCD) films. We employ the attractive Hubbard model within the mean field approximation, including the short-range Coulomb interaction between holes in the narrow acceptor band. We study substitutional boron incorporation in a triangular lattice, with disorder in the form of random potential fluctuations at the boron sites. The role of structural disorder was studied through non-uniform variation of the tight-binding coupling parameter where, following experimental findings, we incorporate the concurrent increase in structural disorder with increasing boron concentration. We illustrate stark differences between the effects of structural and on-site disorder and show that structural disorder has a much greater effect on the density of states, mean pairing amplitude and superfluid density than on-site potential disorder. We show that structural disorder can increase the mean pairing amplitude while the spectral gap in the density of states decreases with states eventually appearing within the spectral gap for high levels of disorder. This study illustrates how the effects of structural disorder can explain some of the features found in superconducting BDD and BNCD films such as a tendency towards saturation of the Tc with boron doping and deviations from the expected BCS theory in the temperature dependence of the pairing amplitude and spectral gap.