Recently, there have been increasing interests in phonon thermal transport in low dimensional materials, due to the crucial importance for dissipating and managing heat in micro and nano electronic devices. Significant progresses have been achieved for one-dimensional (1D) systems both theoretically and experimentally. However, the study of heat conduction in two-dimensional (2D) systems is still in its infancy due to the limited availability of 2D materials and the technical challenges in fabricating suspended samples suitable for thermal measurements. In this review, we outline different experimental techniques and theoretical approaches for phonon thermal transport in 2D materials, discuss the problems and challenges in phonon thermal transport measurements and provide comparison between existing experimental data. Special focus will be given to the effects of the size, dimensionality, anisotropy and mode contributions in the novel 2D systems including graphene, boron nitride, MoS2, black phosphorous, silicene etc.
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