Two-level systems observed in the mechanical properties of single-crystal silicon at low temperatures

Using the high-Q mechanical-oscillator technique we have measured the sound velocity and mechanical dissipation of high-purity single-crystal silicon as functions of temperature (0.005–4.2 K), frequency (0.6–6.0 kHz), and strain amplitude (10-5–10-8). In the mechanical properties we find a surprisingly strong temperature dependence with the same qualitative behavior for silicon as for vitreous silica. This implies a density of two-level systems …