Influence of temperature gradients on tunnel junction thermometry below 1 K: cooling and electron-phonon coupling

TL;DR

This study investigates how temperature gradients develop in thin metallic wires at sub-Kelvin temperatures, using experimental measurements and theoretical modeling to understand their impact on tunnel junction thermometry.

Contribution

It provides new experimental data and a model that accounts for electron-phonon interactions and thermal conductivity, enhancing understanding of thermal behavior in nanoscale wires at very low temperatures.

Findings

Significant temperature gradients can form in short, well-conducting wires at sub-Kelvin temperatures.

Experimental data aligns well with the model including electron-phonon coupling and Wiedemann-Franz law.

Temperature differences are measurable even in short non-heated wire segments.

Abstract

We have studied thermal gradients in thin Cu and AlMn wires, both experimentally and theoretically. In the experiments, the wires were Joule heated non-uniformly at sub-Kelvin temperatures, and the resulting temperature gradients were measured using normal metal-insulator-superconducting tunnel junctions. The data clearly shows that even in reasonably well conducting thin wires with a short ($\sim 10 \mu$m) non-heated portion, significant temperature differences can form. In most cases, the measurements agree well with a model which includes electron-phonon interaction and electronic thermal conductivity by the Wiedemann-Franz law.