Thermal Properties of Mesoscopic Amorphous Membranes
D.-V. ANGHEL, T. KÜHN, Y. M. GALPERIN
Abstract. 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. |