# Influence of Phonon dimensionality on Electron Energy Relaxation

## TL;DR

This study experimentally investigates how phonon dimensionality affects electron-phonon interactions in thin copper wires at sub-Kelvin temperatures, revealing that 2D phonon spectra enhance e-p scattering at very low temperatures.

## Contribution

It provides the first experimental evidence that 2D phonon spectra significantly alter the temperature dependence and strength of electron-phonon interactions in thin metallic wires.

## Key findings

- 2D phonon spectrum changes the temperature dependence of e-p scattering.
- Electron-phonon interaction becomes stronger below 0.5 K in 30 nm membranes.
- Phonon dimensionality influences electron energy relaxation at sub-Kelvin temperatures.

## Abstract

We studied experimentally the role of phonon dimensionality on electron-phonon (e-p) interaction in thin copper wires evaporated either on suspended silicon nitride membranes or on bulk substrates, at sub-Kelvin temperatures. The power emitted from electrons to phonons was measured using sensitive normal metal-insulator-superconductor (NIS) tunnel junction thermometers. Membrane thicknesses ranging from 30 nm to 750 nm were used to clearly see the onset of the effects of two-dimensional (2D) phonon system. We observed for the first time that a 2D phonon spectrum clearly changes the temperature dependence and strength of the e-p scattering rate, with the interaction becoming stronger at the lowest temperatures below $\sim$ 0.5 K for the 30 nm membranes.