Intrinsically Localized Lattice Vibrations in Crystalline Lattices

The formation of Intrinsically Localized Modes (ILMs) for a pair of harmonic phonons along the direction [111] of the Sodium Iodide (NaI) crystalline lattice is examined. The tendency for ILMs to form at a certain center-of-mass momentum q and corresponding relative momentum vector k is attributed to the van-Hove singularities condition in the non-interaction two-phonon density of states continuum. It is observed that, as q converges to the high-symmetry point L=q (π, π, π) of the Brillouin zone, the relative momentum vector k remains invariant at k(π/2, π/2, π/2)  for a certain threshold value of q, and coalesces at the upper-edge of the two-phonon density of states spectrum with high degeneracy in the two-phonon critical energy. It can be concluded that the excitation spectra of the pairs of harmonic phonon excitations become energetically degenerate past the threshold q value towards L at the invariant vector k, announcing the strong presence of ILMs. The calculated ILMs is observed at a critical energy of 20.0 meV for a nearest neighbor and next-nearest neighbor spring coupling constants ratio of 0.598. Reports of Inelastic Neutron Scattering experiments have identified one-phonon breather excitations energy of 10.2 meV at elevated temperatures of 555 K. The formation of ILMs, or multi-phonon bound states, is expected to arise as a result of the anharmonic interactions that lift these degeneracies to enhance the formation of ILMs.