Strongly correlated phonons and the breakdown of phonon theory in MgO and BaTiO₃

The phonon theory of lattice vibrations is exact in the limit of zero temperature. In this limit, phonons are non-interacting; but as the temperature is raised, anharmonic terms in the potential expansion become more important, giving rise to phonon-phonon interactions. If the strength of phonon-phonon interaction increases, strong correlation occurs and phonons themselves can become poorly defined. This can happen at very high temperatures, or in the vicinity of structural phase transitions, in cases exhibiting "rattler modes" in the material (i.e. atoms oscillating between local energy minima). 

We calculate the velocity-velocity correlation function from molecular dynamics simulations, obtaining (omega,k)-resolved power spectra at finite temperatures, to explore the breakdown of phonon theory with temperature in MgO and BaTiO₃. This breakdown is gradual in MgO but there are more sudden changes in BaTiO₃ near its phase transitions, when its central mode, which is a rattler mode, emerges.