Optical absorption by mixed polarons. I. Theory

A theory is developed for optical absorption at low temperatures by polarons which are composed of a mixture of large- and small-radius components. Transitions can involve either type of component of the initial and final states. Hence there are four types of contribution to the absorption. For weak coupling to phonons, the contribution involving the large-polaron components of initial and final states is dominated by one-phonon processes. It consists of two parts, the first commencing at photon energies equal to the relevant phonon energy, and the second at energies higher than this by an amount equal to the energy separation between upper and lower mixed-polaron bands at the band edges. Both these parts commence to rise as the square root of the energy of photons above threshold, and decay approximately as Omega -2.5 for large photon energies Omega . The other three contributions to absorption are dominated by many-phonon processes. Those involving the small-polaron component of the final state have forms similar to those for transitions between two small-polaron bands, while transitions from small-polaron to large-polaron components of states give a weak absorption over a much wider energy range. Changes required in the theory at finite temperatures are discussed briefly.