Conductivity and tunneling density of states in granular Cr films

Abstract

We have measured the tunneling differential conductances, G(V), of four Al/AlOx/Cr planar tunnel junctions as well as the conductivities, sigma(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 similar or equal to 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 ln V law at low bias voltages (less than or similar to a few millielectron volt) while crossing over to a root V law at high bias voltages. Simultaneously, the conductivities of the Cr electrodes reveal ln T dependence below a characteristic temperature. These results are explained in terms of the recent theory of granular metals. In a sample with g similar or equal to 1, in addition to the conductivity dependence sigma proportional to ln T, we observed a universal scaling behavior of the normalized differential conductance [G(V, T) -G(0, T)]/root T with the combined parameter root e vertical bar V vertical bar/k(B)T in a wide temperature interval of 2.5-32 K. This result is not yet understood.