Relation between Johnson Noise and heating power in a two-terminal conductor

TL;DR

This paper derives universal relations linking Johnson noise temperature to heat flux and Joule heating in a two-terminal conductor obeying the Wiedemann-Franz law, providing insights into thermal-electrical noise interactions.

Contribution

It introduces simple, generic relations between Johnson noise temperature and heat flux, applicable to systems with Joule heating or external heat sources, under the Wiedemann-Franz law.

Findings

Universal proportionality between Joule power and Johnson noise temperature increase.

Simple relation between Johnson noise temperature and external heat flux.

Applicability to two-dimensional, two-terminal conductors obeying Wiedemann-Franz law.

Abstract

We consider the Johnson noise of a two-dimensional, two-terminal electrical conductor for which the electron system obeys the Wiedemann-Franz law. We derive two simple and generic relations between the Johnson Noise temperature and the heat flux into the electron system. First, we consider the case where the electron system is heated by Joule heating from a DC current, and we show that there is a universal proportionality coefficient between the Joule power and the increase in Johnson noise temperature. Second, we consider the case where heat flows into the sample from an external source, and we derive a simple relation between the Johnson noise temperature and the heat flux across the boundary of the sample.