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

TL;DR

This paper models how Lamb phonon modes interact with two-level systems in amorphous nanoscopic membranes, revealing a unique temperature dependence of heat conductivity influenced by membrane size and TLS interactions.

Contribution

It introduces a generalized interaction model between Lamb modes and TLSs in amorphous membranes, analyzing their effects on phonon mean free paths and heat conductivity.

Findings

Heat conductivity diverges for infinitely wide membranes.

Finite size imposes a lower frequency cutoff, affecting temperature dependence.

Heat conductivity follows a T + bT   ln T pattern at low temperatures.

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.