Tunneling states in amorphous thin films at low temperatures: Thermal and acoustical properties of amorphous thin films

Abstract

The effects of surface phonons on the tunneling state in amorphous thin films are theoretically investigated at low temperatures. Most accessible to experiment is the case where the amorphous thin film is evaporated onto the solid surface. The attenuation rate of surface phonons is found to be proportional to $\frac{{\omega }^3}{T}$ for surface-phonon frequency small compared to $k_{B}T$. The relative variation of the surface-phonon velocity is also calculated by means of the Kramers-Kronig relation, which shows a frequency and temperature dependence proportional to ${\omega }^2(\frac{1}{T_0}-\frac{1}{T})$. These are quite different from those of the amorphous bulk materials.