Abstract
We measured the acoustic properties of amorphous thin $\mathrm{SiO}{}_{2}$ films with thickness $20\ensuremath{\le}t\ensuremath{\le}500\mathrm{nm}$ in the temperature range $0.1\mathrm{mK}\ensuremath{\le}\mathrm{T}\ensuremath{\le}1\mathrm{K}$ and at frequencies $\ensuremath{\nu}\ensuremath{\sim}10\mathrm{kHz}$. We found that the sound velocity maximum of these films is strongly affected by the film thickness. This unexpected behavior can be attributed to a modification of the phonon mediated interaction between tunneling systems due to the smaller dimensionality of the films, and supports recently published models on the nature of low-energy excitations in amorphous solids.
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