Resistivity and magnetoresistivity measurements near the metal-insulator and superconductor-insulator transition in granular Al-Ge

Granular Al-Ge films just on the metallic side of the critical volume fraction ${\mathrm{\phi }}_{\mathit{c}}$ (50.7% Al) are found to have critical fields in excess of 1.5 T at 0.47 K due to the fine granular nature of the Al. In barely insulating films where (${\mathrm{\phi }}_{\mathit{c}}$-φ)${\mathit{T}}_{\mathit{c}}$ (${\mathit{T}}_{\mathit{c}}$≃1.6 K). For the more insulating films where 3.4%≤(${\mathrm{\phi }}_{\mathit{c}}$-φ)≤6.2%, the resistivity diverges strongly below ${\mathit{T}}_{\mathit{c}}$ and a large negative magnetoresistivity is observed. This behavior is explained in terms of quasiparticle tunneling or alternatively by the Adkins charging model; the magnetoresistivity is explained in terms of a magnetic-field-dependent superconducting energy gap. The upper critical fields of all the samples are found to be almost independent of the bulk resistivities, supporting a picture of weakly coupled grains. The normal resistivity in the insulating films (φ${\mathrm{\phi }}_{\mathit{c}}$) obeys the hopping relation ρ=${\mathrm{\rho }}_0$exp(${\mathit{T}}_0$/T${)}^{\mathit{x}}$ above ${\mathit{T}}_{\mathit{c}}$ and also below ${\mathit{T}}_{\mathit{c}}$ in a field of 3.48 T, which quenches all superconductivity in the films.