Urbach-Martienseen Rule and Exciton Trapped Momentarily by Lattice Vibrations

Theory for the Urbach-Martienssen (U-M) rule on the low energy tail of the fundamental absorption edge of insulators is proposed. The exciton propagator solved for an adiabatic lattice is averaged for lattice vibrations at finite temperature, and the self-energy of exciton is obtained. It describes two characters of exciton in the lattice; the one is the mobile nature of exciton in the undeformed lattice, and the other is the localized nature of exciton trapped momentarily by the lattice deformation due to thermal vibrations. The interplay of the two natures results in the U-M tail below the exciton absorption peak. The result can be interpreted in terms of the Franck-Condon principle where the mobile nature is incorporated in the giant oscillator strength of the momentarily trapped exciton. Emission from this trapped state is discussed in connection with the U-M rule.