Anomalous Heat Conduction and Anomalous Diffusion in Low Dimensional Nanoscale Systems

TL;DR

This paper reviews recent experimental, theoretical, and numerical studies showing that Fourier's law breaks down in low-dimensional nanoscale systems, where heat conduction becomes size-dependent due to super-diffusive phonon transport.

Contribution

It provides a comprehensive overview of the anomalous heat conduction phenomena in low-dimensional systems and highlights the super-diffusive phonon transport as the underlying mechanism.

Findings

Phonon transport in low-dimensional systems is super-diffusive.

Thermal conductivity depends on system size in these systems.

Fourier's law does not hold in low-dimensional nanoscale structures.

Abstract

Thermal transport is an important energy transfer process in nature. Phonon is the major energy carrier for heat in semiconductor and dielectric materials. In analogy to Ohm's law for electrical conductivity, Fourier's law is a fundamental rule of heat transfer in solids. It states that the thermal conductivity is independent of sample scale and geometry. Although Fourier's law has received great success in describing macroscopic thermal transport in the past two hundreds years, its validity in low dimensional systems is still an open question. Here we give a brief review of the recent developments in experimental, theoretical and numerical studies of heat transport in low dimensional systems, include lattice models, nanowires, nanotubes and graphenes. We will demonstrate that the phonon transports in low dimensional systems super-diffusively, which leads to a size dependent thermal conductivity. In other words, Fourier's law is breakdown in low dimensional structures.