Cumulant Methods in the Theory of Multiphonon Absorption

Abstract

Recent studies suggest that multiphonon absorption in covalent solids is substantially influenced by contributions due to nonlinear electric moments. We demonstrate that the dielectric response in the latter case may be formulated in terms of a cumulant series involving lattice displacement correlators, which avoids the usual perturbative expansions of the moment and anharmonic potential in powers of displacements, and thus accounts for various classes of phonon processes to infinite order. To assess the utility of the method we compare results obtained by truncating the cumulant series with exact ones, calculated for a single-particle model. For parameters characteristic of typical binary semiconductors, the harmonic approximation to the cumulant yields poor results. On the other hand, the use of anharmonic correlators is shown to provide good agreement with exact behavior after several terms in the cumulant have been included. Overall, the results suggest that cumulant methods are highly promising for calculating multi-phonon absorption coefficients.