LOW-TEMPERATURE AC CONDUCTIVITY OF ADIABATIC SMALL-POLARONIC HOPPING IN DISORDERED-SYSTEMS

Electronic hopping is commonly treated as occurring between localized states that are so widely separated that the motion is limited by the electronic transfer energy linking the sites. Then, the jump rate is usually assumed to fall exponentially with increasing intersite separation. However, this approach is inappropriate in many situations where the separation between the hopping sites is small enough that electronic carriers adiabatically follow the atomic motion. For adiabatic motion, the jump rates are essentially independent of intersite separation. Here the low-temperature ac conductivity for adiabatic small-polaronic hopping between close pairs of sites is calculated presuming a distribution of local site energies. Low-temperature relaxation of each such carrier is assumed to occur primarily through the emission of a very-low-energy acoustic phonon. For small-polaronic hops, low-temperature one-phonon emission rates are extremely slow. Dispersion of the transition rates arises from the dependence of the relaxation rates on the energy separations between the sites. In the low-temperature limit, the polarization conductivity is proportional to both temperature and frequency. Above this low-temperature limit, the severity of this temperature dependence increases with increasing temperature. In this higher-temperature regime, the temperature dependence of the conductivity also decreases as the frequency is increased. These results are in accord with observations in many systems with hopping conduction, including those for which there is explicit evidence of adiabatic small-polaronic hopping (e.g., p-type MnO, boron carbides, and many transition-metal-oxide glasses).