Stability Dependence of the Vibrational Properties of Glasses in Two and Three Dimensions*

To understand why the universal low-temperature properties of glasses
differ dramatically from their crystalline counterparts, it is paramount
to understand what controls the vibrational properties of glasses. Numerical
methods generally create glasses by quenching a mildly supercooled liquid,
which limits the variation of vibrational properties of glasses and the
ability to examine correlations between different quantities.
Due to recent advances in simulation techniques, we are now able to study glasses
with a wide range of stabilities. Additionally, since
there is evidence that the glass transition and vibrational properties of
glasses are different in two and three dimensions, understanding these differences
can aid in the understanding of the low-temperature properties of glasses.
Here, we study vibrational modes and sound attenuation in simulated glasses
that range from very poorly annealed to very stable. Our most
stable glass is comparable to exceptionally-stable, vapor-deposited
laboratory glasses.
In both two and three dimensions we find that the density of the
quasi-localized, low-frequency
modes decrease quickly with increasing stability.
Notably the quasi-localized, low-frequency modes in two dimensions are
nearly absent for the most stable glasses.
Accompanying this large decrease
in quasi-localized, low-frequency modes is a large decrease in sound attenuation with
increasing stability.
We contrast the difference in the scaling of the
boson peak height and frequency in two and three dimensions.