The nonuniversality of the frequency dependence of the conductivity in disordered nanogranulated systems

The real part of the high-frequency phononless conductivity is calculated in the pair approximation for a disordered array of densely packed spherical nanogranules. The generalization of the theory of phononless conductivity for systems with point impurities to systems with localized finite sizes (arrays of nanogranules or quantum dots) reveals that the high-frequency conductivity depends on the distribution function of the distances between the surfaces of granules $P(w)$. This is expected to cause the discrepancy of the real part of the conductivity $\sigma_1(\omega)$ from the linear frequency dependence. In the vicinity of the frequency $\omega\sim\omega_{c} = 2I_{0}/\hbar$ ($I_{0}$ is a preexponential factor of the resonance integral) for disordered granulated systems is likely to deviate from the universality $\sigma_1(\omega)\sim\omega^s$ ($s\approx$ 1) due to the attenuation of the frequency dependence $\sigma_1(\omega)$ of the conductivity and its nonmonotonicity. The nonmonotonicity of $\sigma_1(\omega)$ must arise at lower frequencies as a result of decreased preexponential factor $I_0$ of the resonance integral with increasing granule size.