Interaction of Lamb modes with two-level systems in amorphous nanoscopic membranes

Using a generalized model of interaction between a two-level system (TLS) and an arbitrary deformation of the material, we calculate the interaction of Lamb modes with TLSs in amorphous nanoscopic membranes. We compare the mean free paths of the Lamb modes of different symmetries and calculate the heat conductivity kappa. In the limit of an infinitely wide membrane, the heat conductivity is divergent. Nevertheless, the finite size of the membrane imposes a lower cutoff for the phonon frequencies, which leads to the temperature dependence kappa proportional to T(a+b ln T). This temperature dependence is a hallmark of the TLS-limited heat conductance at low temperature.