Graphene exhibits extraordinary electronic and mechanical properties, and extremely high thermal conductivity. Being a very stable atomically thick membrane that can be suspended between two leads, graphene provides a perfect test platform for studying thermal conductivity in two-dimensional systems, which is of primary importance for phonon transport in low-dimensional materials. Here we report experimental measurements and non-equilibrium molecular dynamics simulations of thermal conduction in suspended single-layer graphene as a function of both temperature and sample length. Interestingly and in contrast to bulk materials, at 300 K, thermal conductivity keeps increasing and remains logarithmically divergent with sample length even for sample lengths much larger than the average phonon mean free path. This result is a consequence of the two-dimensional nature of phonons in graphene, and provides fundamental understanding of thermal transport in two-dimensional materials.

Interfacial thermal resistance (ITR) is the main obstacle for heat flows from one material to another. Understanding ITR becomes essential for the removal of redundant heat from fast and powerful electronic and photonic devices, batteries, etc. In this review, a comprehensive examination of ITR is conducted. Particular focus is placed on the theoretical, computational, and experimental developments in the 30 years after the last review given by Swartz and Pohl in 1989. To be self-consistent, the fundamental theories, such as the acoustic mismatch model, the diffuse mismatch model, and the two-temperature model, are reviewed. The most popular computational methods, including lattice dynamics, molecular dynamics, the Green’s function method, and the Boltzmann transport equation method, are discussed in detail. Various experimental tools in probing ITR, such as the time-domain thermoreflectance, the thermal bridge method, the $3\omega$ method, and the electron-beam self-heating method, are illustrated. This review covers ITR (also known as the thermal boundary resistance or Kapitza resistance) of solid-solid, solid-liquid, and solid-gas interfaces. Such fundamental challenges as how to define the interface, temperature, etc. when the materials scale down to the nanoscale or atomic scale and the opportunities for future studies are also pointed out.