Anomalous Size Dependence of the Thermal Conductivity of Graphene Ribbons

TL;DR

This paper presents a theoretical study on how the thermal conductivity of graphene ribbons and graphite slabs depends on their size, revealing an unusual non-monotonic behavior due to phonon mean free paths and edge effects.

Contribution

The study introduces a model considering anharmonic phonon processes and edge scattering, explaining the anomalous size dependence of thermal conductivity in graphene and graphite.

Findings

Thermal conductivity of graphene ribbons shows non-monotonic size dependence.

Bulk-like phonons significantly contribute to graphite's in-plane thermal conductivity.

Scaling laws for thermal conductivity with size are established for graphene and graphite.

Abstract

We investigated the thermal conductivity K of graphene ribbons and graphite slabs as the function of their lateral dimensions. Our theoretical model considered the anharmonic three-phonon processes to the second-order and included the angle-dependent phonon scattering from the ribbon edges. It was found that the long mean free path of the long-wavelength acoustic phonons in graphene can lead to an unusual non-monotonic dependence of the thermal conductivity on the length L of a ribbon. The effect is pronounced for the ribbons with the smooth edges (specularity parameter p>0.5). Our results also suggest that - contrary to what was previously thought - the bulk-like 3D phonons in graphite can make a rather substantial contribution to its in-plane thermal conductivity. The Umklapp-limited thermal conductivity of graphite slabs scales, for L below ~ 10 micrometers, as log(L) while for larger L, the thermal conductivity approaches a finite value following the dependence K_0 - A\timesL^-1/2, where K_0 and A are parameters independent of the length. Our theoretical results clarify the scaling of the phonon thermal conductivity with the lateral sizes in graphene and graphite. The revealed anomalous dependence K(L) for the micrometer-size graphene ribbons can account for some of the discrepancy in reported experimental data for graphene.