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It is widely accepted that structural glasses and disordered crystals exhibitanomalies in the their thermal, mechanical and acoustic properties asmanifestations of the breakdown of the long-wavelength approximation in adisordered dissipative environment. However, the same type of glassy-likeanomalies (i.e. boson peak in the vibrational density of states (VDOS) abovethe Debye level, peak in the normalized specific heat at $T\simeq10 K$ etc)have been recently observed also in perfectly ordered crystals, includingthermoelectric compounds. Here we present a theory that predicts thesesurprising effects in perfectly ordered crystals as a result of low-lying(soft) optical phonons. In particular, it is seen that a strong boson peakanomaly (low-energy excess of modes) in the VDOS can be due almost entirely tothe presence of low-energy optical phonons, provided that their energy iscomparable to that of the acoustic modes at the Brillouin zone boundary. Theboson peak is predicted also to occur in the heat capacity at low $T$. Inpresence of strong damping (which might be due to anharmonicities in theordered crystals), these optical phonons contribute to the low-$T$ deviationfrom Debye's $T^{3}$ law, producing a linear-in-$T$ behavior which is typicalof glasses, even though no assumptions of disorder whatsoever are made in themodel. These findings are relevant for understanding and tuning thermaltransport properties of thermoelectric compounds, and possibly for theenhancement of electron-phonon superconductivity.

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