Low-Temperature Heat Transport under Phonon Confinement in Nanostructures

TL;DR

This paper presents a computational model for phonon heat transport in nanostructures under confinement at low temperatures, validated with experiments on superconducting nanostructures, highlighting implications for cryogenic device performance.

Contribution

The authors develop a new computational approach to model phonon heat capacity and transport rates in confined geometries, addressing a gap in existing theories for cryogenic nanodevices.

Findings

Confinement reduces heat capacity significantly.

Heat transport can be slowed down due to confinement effects.

Model validated with experiments on NbTiN superconducting nanostructures.

Abstract

Heat transport in bulk materials is well described using the Debye theory of 3D vibrational modes (phonons) and the acoustic match model. However, in cryogenic nanodevices, phonon wavelengths exceed device dimensions, leading to confinement effects that standard models fail to address. With the growing application of low-temperature devices in communication, sensing, and quantum technologies, there is an urgent need for models that accurately describe heat transport under confinement. We introduce a computational approach to obtain phonon heat capacity and heat transport rates between solids in various confined geometries, that can be easily integrated into, e.g., the standard two-temperature model. Confinement significantly reduces heat capacity and may slow down heat transport. We have validated our model in experiments on strongly disordered NbTiN superconducting nanostructures, widely used in highly efficient single-photon detectors, and we argue that confinement is due to their polycrystalline granular structure. These findings point to potential advances in cryogenic device performance through tailored material and microstructure engineering.