Optical absorption of free small polarons at high temperatures

The real part of high-frequency electrical conduction, or the optical absorption, of free small polarons at high temperatures is calculated. The spectrum exhibits a slightly asymmetric Gaussian shape. Comparing with the previous theories, the peak position shifts toward lower energies and there exists an additional broadening of the line shape due to the distribution of localized energy levels. The results also show that the temperature dependence of the dc conductivity is more complicated than previously indicated. A quantitative agreement between theory and experiment is given. Application of this theory to bound small polarons is discussed.