Dielectric Susceptibility and Infrared Absorption in an Anharmonic Crystal

Abstract

Using the method of temperature-dependent double-time Green's function, an expression is obtained for the dielectric susceptibility of an anharmonic crystal considering second-order terms in the dipole moment expansion and third- and fourth-order anharmonic terms in the crystal potential energy. The polarization operator and the phonon Green's function are evaluated in two successive approximations by means of equivalent renormalized Hamiltonian using Dyson's equation for the phonon spectrum. The results are used to obtain an expression for the frequency and temperature dependence of the coefficient of infrared of optical absorption. It is shown that in the high temperature region, the width of the fundamental lattice absorption peak is the sum of two terms proportional to the first and second powers of the absolute temperature in conformity with experiments. The results obtained are general and are applicable to the ionic crystals as well as to covalent crystals, where the linear dipole moment is zero.