Low-Frequency Vibrational Modes of Stable Glasses

There is an excess in the vibrational density of states g(ω) over Debye scaling at low-frequencies, the so-called Boson peak, which results in a peak in g(ω)/ω². We examine the low-frequency density of states of glasses obtained from quenching supercooled liquids equilibrated at parent temperatures T between temperatures above the onset of supercooling to 62% of the mode coupling temperature T_C. The kinetic stability of the glasses at the lowest temperatures examined are comparable to that of experimental glasses. We divide the low-frequency density of states into phonon and quasi-localized modes. We show that the phonon density of states g_D(ω) obeys Debye scaling, g_D(ω) = A_Dω², where A_D is the Debye level estimated from the sound velocities. We also show that the quasi-localized density of states obeys g₄(ω) = A₄ω⁴ for each T. For parent temperatures above T_C, A_D and A₄ weakly depend on T. For parent temperatures below T_C, both A_D and A₄ decrease with decreasing T, with A_D decreasing around 30% and A₄ decreasing by an order of magnitude. Additionally, we find that height of the Boson peak scaled by the Debye level A_D is independent of T.