Electron heating in metallic resistors at sub-Kelvin temperature

TL;DR

This paper provides a comprehensive solution for understanding electron heating in metallic resistors at sub-Kelvin temperatures, focusing on temperature profiles, noise characteristics, and time-dependent effects relevant for low-temperature experiments.

Contribution

It introduces a general, practical solution for electron temperature profiles considering Joule heating, electron diffusion, and phonon coupling, applicable to various experimental setups.

Findings

Derived explicit formulas for electronic temperature profiles.

Analyzed current noise cumulants as functions of voltage.

Studied effects of time-dependent heating in pulsed experiments.

Abstract

In the presence of Joule heating, the electronic temperature in a metallic resistor placed at sub-Kelvin temperatures can significantly exceed the phonon temperature. Electron cooling proceeds mainly through two processes: electronic diffusion to and from the connecting wires and electron-phonon coupling. The goal of this paper is to present a general solution of the problem, in a form that can easily be used in practical situations. As an application, we compute two quantities that depend on the electronic temperature profile: the second and the third cumulant of the current noise at zero frequency, as a function of the voltage across the resistor. We also consider time dependent heating, an issue relevant for experiments in which current pulses are used, for instance in time-resolved calorimetry experiments.