Universality of the electrical transport in granular metals

The universality of the ac electrical transport in granular metals has been scarcely studied and the actual mechanisms involved in the scaling laws are not well understood. Previous works have reported on the scaling of capacitance and dielectric loss at different temperatures in Co-ZrO2 granular metals. However, the characteristic frequency used to scale the conductivity spectra has not been discussed, yet. This report provides unambiguous evidence of the universal relaxation behavior of Pd-ZrO2 granular thin films over wide frequency (11 Hz-2 MHz) and temperature ranges (40-180 K) by means of Impedance Spectroscopy. The frequency dependence of the imaginary parts of both the impedance Z″ and electrical modulus M″ exhibit respective peaks at frequencies ωmax that follow a thermal activation law, ωmax ∝ exp(T(1/2)). Moreover, the real part of electrical conductivity σ' follows the Jonscher's universal power law, while the onset of the conductivity dispersion also corresponds to ωmax. Interestingly enough, ωmax can be used as the scaling parameter for Z″, M″ and σ', such that the corresponding spectra collapse onto single master curves. All in all, these facts show that the Time-Temperature Superposition Principle holds for the ac conductance of granular metals, in which both electron tunneling and capacitive paths among particles compete, exhibiting a well-characterized universal behavior.