Impurity effects on optical response in a finite-band electronic system coupled to phonons

The concepts which have traditionally been useful in understanding the effects of the electron-phonon interaction in optical spectroscopy are based on insights obtained within the infinite-electronic-band approximation and no longer apply in finite-band metals. Impurity and phonon contributions to electron scattering are not additive and the apparent strength of the coupling to the phonon degrees of freedom is substantially reduced with increased elastic scattering. The optical mass renormalization changes sign with increasing frequency and the optical scattering rate never reaches its high-frequency quasiparticle value, which itself is also reduced below its infinite-band value.