Emergence of Fourier's law of heat transport in quantum electron systems

TL;DR

This paper investigates how Fourier's law of heat transport naturally emerges in quantum electron systems, especially when many quantum states participate, using a graphene flake junction as a test case.

Contribution

It proposes that Fourier's law arises from many quantum states participating in heat transport and develops a thermal resistor network model to explain the transition to classical behavior.

Findings

Temperature distribution becomes nearly classical with large state broadening.

Thermal contact resistance aligns with classical theory at high level broadening.

The model explains the emergence of Fourier's law in quantum systems.

Abstract

The microscopic origins of Fourier's venerable law of thermal transport in quantum electron systems has remained somewhat of a mystery, given that previous derivations were forced to invoke intrinsic scattering rates far exceeding those occurring in real systems. We propose an alternative hypothesis, namely, that Fourier's law emerges naturally if many quantum states participate in the transport of heat across the system. We test this hypothesis systematically in a graphene flake junction, and show that the temperature distribution becomes nearly classical when the broadening of the individual quantum states of the flake exceeds their energetic separation. We develop a thermal resistor network model to investigate the scaling of the sample and contact thermal resistances, and show that the latter is consistent with classical thermal transport theory in the limit of large level broadening.