A first-principles investigation of the transition between two- and three-dimensional thermal transport in graphene and graphite

Abstract

Two-dimensional materials have become a popular research area over the past two decades because of their unique physical properties. The low dimensionality of these materials leads to interesting, and useful, transport properties such as thickness-dependent band gaps and high electrical and thermal conductivity. These materials have applications in nanoelectronics, optoelectronics, and thermoelectric energy generation, the performance of which depends sensitively on understanding and controlling how heat transport occurs.

Most low dimensional materials can be derived by isolating them from their bulk counterparts, which are often comprised of stacks of the two-dimensional layers that are weakly bound together. These layered bulk materials often maintain some of the two-dimensional characteristics of their monolayer form because of the weak interlayer bonds. One common example of such a “quasi-2D” material is graphite, which is made of layered carbon sheets, i.e. graphene. When going from graphite to graphene the room-temperature in-plane thermal conductivity varies from approx. 2000 W/m K to 5800 W/m K, respectively. Both values are exceptionally high, but there is still a large difference between the two. Nevertheless, the majority of studies focus either on the bulk or low-dimensional versions of materials, with little focus on how the transition from 3D to 2D influences the microscopic properties and transport characteristics.

The purpose of this study was to explain how the thermal transport properties of layered materials transition between two and three dimensions. Graphene and graphite were used as simple materials to model this transition. The thermal transport properties were calculated from first-principles using density functional theory (DFT) and iterative solutions to the Boltzmann transport equation (BTE). The transition between two and three dimensions was modelled by systematically moving the layers of graphite apart from each other until they were essentially isolated graphene sheets.

The converged $\kappa$ values of the limiting cases of graphite and graphene agree with experimental measurements and previous calculations, with the stretched cases showing a monotonically increasing thermal conductivity from $\kappa_{\text{graphite}}$ to $\kappa_{\text{graphene}}$. Surprisingly, the largest variation in the thermal transport properties resulted from changes in the phonon dispersion. This is contrary to the previous belief that the difference in $\kappa$ resulted from certain three-phonon selection rules in graphene, which reduce the scattering probability, and do not apply to graphite. The selection rules appear to mostly still apply to graphite and the stretched graphite cases, indicating that the primary mechanism resulting in the differences between $\kappa_{\text{graphene}}$ and $\kappa_{\text{graphite}}$ was the shape of the phonon dispersion, and a corresponding shift in the phonon DOS. This type of analysis could be applied to other layered materials in the future to identify materials with the potential to be exceptional thermal conductors.