Tuning the Correlation Decay in the Resistance Fluctuations of Multi-Species Networks

A new network model is proposed to describe the $1/f^\alpha$ resistance noise in disordered materials for a wide range of $\alpha$ values ($0< \alpha < 2$). More precisely, we have considered the resistance fluctuations of a thin resistor with granular structure in different stationary states: from nearly equilibrium up to far from equilibrium conditions. This system has been modelled as a network made by different species of resistors, distinguished by their resistances, temperature coefficients and by the energies associated with thermally activated processes of breaking and recovery. The correlation behavior of the resistance fluctuations is analyzed as a function of the temperature and applied current, in both the frequency and time domains. For the noise frequency exponent, the model provides $0< \alpha < 1$ at low currents, in the Ohmic regime, with $\alpha$ decreasing inversely with the temperature, and $1< \alpha <2$ at high currents, in the non-Ohmic regime. Since the threshold current associated with the onset of nonlinearity also depends on the temperature, the proposed model qualitatively accounts for the complicate behavior of $\alpha$ versus temperature and current observed in many experiments. Correspondingly, in the time domain, the auto-correlation function of the resistance fluctuations displays a variety of behaviors which are tuned by the external conditions.