Multi-level Kondo effect and enhanced critical temperature in nanoscale granular Al

The normal state conductance of high resistivity granular Al films, having an enhanced critical temperature above 3 K, shows a non-monotonous temperature dependence. Upon cooling the conductance first increases, reaches a broad maximum, then decreases, and finally increases sharply again at low temperatures. This behavior bears a striking resemblance to that predicted for the conductance of quantum dots in a regime where the broadening of discrete energy levels, due to coupling of the dot to the leads reservoirs, is larger than the level separation. In this regime, a multi-level Kondo temperature can be larger than the effective Coulomb charging energy, leading to a metallic-like behavior at high temperatures. This is followed by a Coulomb dominated regime, while at yet lower temperatures, the single level Kondo behavior can be recovered. We believe that this multi-level Kondo resonance model for single dots may apply to our 3D network of nanoscale grains. The multi-level resonance prevents the insulating state from setting-in already at high temperatures, which is favorable for superconductivity. This interpretation of the experimental conductance data is in line with the previously reported presence of magnetic moments in these films. High-resolution electron microscopy shows that intergrain coupling can take place through atomic size Sharvin contacts, which is consistent with the typical values of the intergrain resistance of the films as the metal to insulator transition is approached.