Soft optical phonons induce glassy-like vibrational and thermal anomalies in ordered crystals

It is widely accepted that structural glasses and disordered crystals exhibit anomalies in the their thermal, mechanical and acoustic properties as manifestations of the breakdown of the long-wavelength approximation in a disordered dissipative environment. However, the same type of glassy-like anomalies (excess of modes in the phonon density of states above the Debye level, peak in the specific heat at $T\simeq10 K$ etc) have been recently observed also in perfectly ordered crystals. Here we present a theory that predicts these surprising effects in perfectly ordered crystals as a result of low-lying soft optical phonons. In particular, it is seen that a strong boson peak anomaly in the vibrational density of states can be due almost entirely to the presence of soft optical phonons, provided that these optical phonons have a sufficiently low energy comparable to that of the acoustic modes at the Brillouin zone boundary. The boson peak is predicted also to occur in the heat capacity at low T. In presence of strong damping (which might be due to anharmonicities in the ordered crystals), soft optical phonons contribute to the low-T deviation from Debye's $T^{3}$ law, producing a linear-in-$T$ behavior which is typical of glasses, even though no assumptions of disorder whatsoever are made in the model.