Small polarons and polaron transitions

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Abstract
The Mott–Littleton method is used mainly for ionic defects in polar crystals, yet it provides a powerful tool for small polarons. These electronic carriers, important in many halides and oxides, cause a substantial self-trapping distortion, and move by an incoherent thermally activated hopping motion. The Mott–Littleton method is important in four ways. The relaxation energy causing self-trapping can be calculated, as for and ionic defect. The activation energy for hopping motion can be rewritten as the difference between two relaxation energies, so the same approach can be used. Similarly, in principle, the barrier to self-trapping may be obtained. Finally, optical transitions of small polarons (effectively charge-transfer transitions) can be estimated since they are dominated by relaxation energies. In practice, there are several problems. Key energies can be small (activation energies are 0.1–0.5 eV) and barriers to self-trapping even smaller. Results are sensitive to potentials for unconventional ionic charge states (e.g. Cl1/2––Cl1–), and the shell model is barely adequate for these electronic structures. The expressions relating activation energy and relaxation energies are based on the harmonic approximation, and relation to observation (which is complicated by the narrow temperature ranges available) involves restrictive assumptions about the phonon density of states.

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