Low-temperature Heat Transport under Phonon Confinement

Abstract

Heat transport in crystalline bulk materials is well understood through the Debye theory of three-dimensional (3D) vibrational modes (phonons) and kinetic equation. In nanodevices at low temperatures, device dimensions are comparable to the phonon wavelengths that introduces confinement, i.e. the reduction of allowed phonon modes. We have recently shown [1] that confinement drastically affects not only the phonon heat capacity of a two-dimensional nanostrip, which has long been known [2], but also the heat flow from such nanodevice to 3D underlying media. To study heat outflow, we implemented the technique of the self-heating normal domain in a superconducting nanostrip on a dielectric substrate [3] and varied external magnetic field thus shifting the superconducting transition temperature. This approach allows one to reconstruct temperature dependences of the phonon heat capacity of the strip and thermal flux through the film/substrate interface. In order to quantitatively describe experimental results, we applied a dedicated model of heat flow [1], which accounts for phonon confinement in granules of a thin metal film. The confinement imposed by granules causes angular dependent cut-off (forbidden states) in the phonon density of states in the momentum space with a position inversely proportional to the mean size of granules. Consequently, phonons with wavevectors smaller that this cut-off are not excited in the film and do not contribute to the heat outflow. The model developed in [1] implies local thermal equilibrium of phonons, so called diffusion approximation or kinetic-equation approximation. Here we will report on the limitations of this model and its possible extension for the case of the ballistic heat transport. This study is motivated by the fact that the mean free path of acoustic phonon, which is set by the phonon-electron interaction time and the phonon velocity, appears close to the mean size of granules. We will discuss possible experimental arrangements where the impact of ballistic transport can be observed experimentally.