Thermal Properties of Mesoscopic Amorphous Membranes

We calculate the thermal properties of nanoscopic amorphous membranes in a temperature range below 1 K. For this we describe the phonon modes in the membrane, which are the eigenmodes of the elastic equations, for the given geometry. With these modes we calculate the heat capacity of the membrane and the heat conductivity. Analytical expressions for these quantities are given in the low temperature range.
To describe the interaction of general phonon modes with the disorder of the material – the dynamical defects –, we extend the standard model (the so called standard tunneling model, STM) by giving a more general formulation to the interaction hamiltonian, which associate a direction to the defects and takes into account orientation of the defect with respect to the local strain field of the phonon. In the end, we recover the results of the STM by averaging over the orientations of the defects. Some values for the parameters of the model were calculated from the experimental data.