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

Abstract

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 with 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 cut-off for the phonons frequencies, which leads to the temperature dependence $\kappa \propto T(a+b\ln T)$. This temperature dependence is a hallmark of the TLS-limited heat conductance at low temperature.

9 pages, 2 figures

References in corpus (3)

• Heat transport in ultra-thin dielectric membranes and bridges
• Interaction of two level systems in amorphous materials with arbitrary phonon fields
• Quantization of the elastic modes in an isotropic plate

Cited by in corpus (8)

• Damping and decoherence of a nanomechanical resonator due to a few two level systems
• Cavity cooling of a mechanical resonator in the presence of two-level-system defects
• Low-temperature electron-phonon heat transfer in metal films
• The Universality of Thermal Transport in Amorphous Nanowires at Low Temperatures
• Maximizing phonon thermal conductance for ballistic membranes
• Crossover in the electron-phonon heat exchange in layered nanostructures
• Anisotropic interaction of two-level systems with acoustic waves in disordered crystals
• Anisotropic glass-like properties in tetragonal disordered crystals