Conductivity and tunneling density of states in granular Cr films

We have measured the tunneling differential conductances, G (V), of four Al/ AlOx /Cr planar tunnel junctions as well as the conductivities, σ (T), of the Cr electrodes at liquid-helium temperatures. The Cr electrodes were made to be granular with dimensionless intergrain tunneling conductance spanning from g≃1 to g≫1, and the dimensionality of the granular array d=3. For the samples with g≫1, we found that the measured G (V) curves display large zero-bias singularities which obey a lnV law at low bias voltages (≲ a few millielectron volt) while crossing over to a √V law at high bias voltages. Simultaneously, the conductivities of the Cr electrodes reveal lnT dependence below a characteristic temperature. These results are explained in terms of the recent theory of granular metals. In a sample with g≃1, in addition to the conductivity dependence σ∞lnT, we observed a universal scaling behavior of the normalized differential conductance [G (V,T) -G (0,T)] /√T with the combined parameter √ e |V| / kB T in a wide temperature interval of 2.5-32 K. This result is not yet understood.