Emergence of Fourier’s Law of Heat Transport in Quantum Electron 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.

Effect of quantum resonances on local temperature in nonequilibrium open systems

“…Instead, the linear profile of T * i is associated with the substantial broadening of the spectral peaks in A(ω). 5 This means that the thermal transport process involves electronic states in a wide range of energies. The phases of these states are averaged out when T * i are measured, which leads to a classical-like behavior.…”

“…Inui et al 5 have reported strong oscillations of temperature distribution in a graphene flake weakly coupled to the electrodes under a thermal bias due to quantum interference. But in their study the local temperatures T * ,ZCC i still remain constant on a relatively small scale in the weak-coupling regime, similar to the curve of T * ,ZCC i in Fig.…”

Local temperatures out of equilibrium

“…To address this issue, Inui et al have studied the Fourier's law in graphene flakes subjected to a thermal bias [433]. Figure 38 shows the calculated local temperature distribution for two different graphene-electrode contact geometries [433]. In the type I contact only the left and right edges of the flake couple to the electrodes, while for type II contact two electrodes cover three edges of the flake, leading to a stronger coupling.…”

“…The local temperature distributions for type I contact exhibit strong oscillations that depend on µ 0 , while for type II contact, the distributions resemble the classical distribution. Reprinted with permission from [433]. Copyright 2018 American Chemical Society.…”

“…The DOS for the type I contact exhibits a sequence of sharp peaks, while the type II contact exhibits a smooth, nearly featureless DOS. Reprinted with permission from [433]. Copyright 2018 American Chemical Society.…”