Crossover between transport mechanisms in the region of the transition from sublinearity to superlinearity of the AC-conductivity frequency dependence for disordered semiconductors

The transition of the frequency dependence of AC conductivity of disordered semiconductors from sublinear to superlinear behavior with an increase in frequency, which is observed for many disordered systems, is investigated. It is shown that the standard approach to calculating the superlinearity of the frequency dependence of the AC hopping conductivity in the form $\operatorname{Re}\sigma(\omega)\sim\frac{\omega}{\ln(\omega_{\mathrm{c,ph}}/\omega)}$ ($\omega_{\mathrm{c,ph}}$ is the characteristic frequency), based on the single-particle density of states with a Coulomb gap, generally cannot be used to calculate high-frequency conductivity. The superlinearity of the experimentally observed frequency dependences of the conductivity $\operatorname{Re}{\sigma(\omega)}$ in the crossover region indicates that the optimal hop length is frequency-independent and that the resonance mechanism of conductivity plays a key role. The resonance mechanism causes abnormally large measured values $\cot(\gamma)=\operatorname{Im}\sigma/\operatorname{Re}\sigma$ ($\gamma$ is the dissipation factor) in the crossover region.