Coupling of quasi-localized and phonon modes in glasses at low frequency

Boson peak of glasses,a THz vibrational excess compared to Debye squared-frequency law,remains mysterious in condensed-matter physics and material science.It appears in many different kinds of glassy matters and is also argued to exist in damped crystals.A consensus is that boson peak originates from the coupling of the(quasi)-localized non-phonon modes and the plane-wave-like phonon modes,but the coupling behavior is still not fully understood.In this paper,by modulating the content of localized modes and the frequencies of phonon modes,the coupling is clearly reflected in the localization and anharmonicity of low-frequency vibrational modes.The coupling enhances with increasing cooling rate and sample size.For finite sample size,phonon modes do not fully intrude into the low frequency to form a dense spectrum and they are not sufficiently coupled to the localized modes,thus there is no Debye level and boson peak is ill-defined.This suggestion remains valid in the presence of thermal motions induced by temperature,even though the anharmonicity comes into play.Our results point to the coupling of quasi-localized and phonon modes and its relation to the boson peak.