Theory of Anharmonic Phonons

Abstract

The harmonic approximation truncates the expansion of the total energy in powers of atomic displacements to second-order and so the collective excitations of the lattice known as phonons are independent and non-interacting. The frequencies of harmonic phonons are well-defined and as a result have infinite lifetimes, they never decay and propagate freely through perfect infinite crystals without impingement or attenuation. Since intrinsic dielectric absorption is known to be a phenomenon associated with interacting phonons, the harmonic approximation will clearly be unable to describe it and that the inclusion of higher order anharmonic terms in the energy expansion will be required. Anharmonic phonons couple and exchange energy with each other, allowing non-equilibrium phonon populations and their associated relaxation phenomena to exist. In going from a harmonic description to an anharmonic one, the real-valued eigenfrequency of the harmonic mode is perturbed and suffers a complex frequency shift shown as the self-energy. This manifests as a real frequency shift and a broadening in the linewidth of the phonon which is measurable using neutron diffraction spectroscopy.