Critical-field anisotropy and fluctuation conductivity in granular aluminum films

Abstract

We have measured the upper critical field ${H}_{c2}(\ensuremath{\theta})$ for extreme type-II granular aluminum films much thicker than the coherence length and have found them to display a strong temperature-dependent anisotropy ($\frac{{H}_{\ensuremath{\parallel}}}{{H}_{\ensuremath{\perp}}}\ensuremath{\gg}1$). The temperature dependence of the parallel critical field, ${H}_{\ensuremath{\parallel}} (T)$, shows an infinite slope near ${T}_{c}$, which we interpret as an indication that these films have a layered structure. The perpendicular critical field, ${H}_{\ensuremath{\perp}}(T)$, has an upward curvature, reminiscent of the behavior observed in ${(\mathrm{SN})}_{x}$ and some layered compounds. As a result, the anisotropy ratio decreases strongly as the temperature is lowered. We interpret this behavior as a transition towards zero dimensionality (decoupled grains). We have also measured the fluctuation conductivity ${\ensuremath{\sigma}}_{s}$ above ${T}_{c}$. We find that, for films with high values of normal-state resistivity, ${\ensuremath{\sigma}}_{s}$ follows a power law characteristic of zero dimensionality far above ${T}_{c}$, and characteristic of two dimensionality closer to ${T}_{c}$, in agreement with the proposed interpretation of the critical-field data.