Heat transport in resonant condensed systems: Thermal conductivity reduction by coherent mechanisms

The notion of a locally resonant metamaterial—widely applied to light and sound—has recently been introduced to heat, whereby the thermal conductivity is reduced primarily by intrinsic localized atomic vibrations (vibrons) rather than scattering mechanisms. The localized vibration modes manifest by the introduction of intrinsic nanoresonators within, or attached to, a host crystalline material, ideally a semiconductor. The phonon band structure under such conditions exhibit a myriad of horizontal bands representing each resonant degree of freedom. These bands hybridize with the underlying phonon modes carrying the heat in the host medium, which leads to significant reductions in the phonon group velocities and to mode localizations within the nanoresonators. Moderate reductions in the phonon lifetimes also occur. The nature of nanoscale thermal conduction under such conditions is fundamentally transformed due to these effects. A key requirement for the realization of phonon-vibron couplings and the subsequent effects mentioned above is the presence of a sufficient level of coherent wave behavior, which is only possible when there is a relatively wide distribution of the phonon mean free path. An example of a “nanophononic metamaterial” is a silicon membrane with nanopillars distributed on the surface. In this work, we provide predictions—by theory and simulations—of the thermal transport properties of this system.