Investigating evidence of intrinsically localized vibrations in NaI crystal using van-Hove singularities of the two-phonon density of states

Intrinsically localized modes (ILMs) are reported in NaI and exist only for wave-vectors at the corner of the 3-D Brillouin Zone. ILMs occur for high-symmetry values, q at which the van-Hove singularities of the two-phonon density of states (DOS) coalesce. The basis for this suggestion is that anharmonic interactions together with the rapid variation of the two-phonon DOS near the band edge may result in the preferential formation of ILMs at these q values. We investigate the van-Hove singularities in the two-phonon DOS, using the experimentally determined acoustic phonon modes ratio of nearest neighbor and next-nearest neighbor force constants. We obtained the two-phonon DOS spectrum for various q in the harmonic approximation and found that they exhibit non-divergent van-Hove singularities. The frequencies of these features vary as q is varied. We found the q value, which mostly enhanced the two-phonon DOS. Furthermore, we isolated the energy and related variable momentum values at which the two-phonon DOS coalesce at the upper edge of the continuum. Now we introduce anharmonic interactions and investigate whether that can bind the two-phonon excitations to produce a quantized ILM.