Specific features of the frequency dependence of the conductivity of disordered semiconductors in the region of the crossover between transport mechanisms

The specific features of the frequency dependence of the impedance of disordered semiconductors at low temperatures for the hopping conduction mechanism are analyzed. Emphasis is placed on the observed discrepancies between the experimental data and the available theory for the frequency dependence of the real part of the conductivity $\sigma_1(\omega)$ in the region of crossover from a linear dependence to a quadratic dependence (the kink in the dependence of $\ln\sigma_1$ on $\ln\omega$) and for anomalously large values of $\cot\gamma$ ($\gamma$ is the dielectric loss angle) measured experimentally. These discrepancies can be described on the basis of an approach that takes into account both the phonon and resonance contributions to the conductivity as well as the transition to the fixed-range hopping conduction at frequencies higher than the crossover frequency.