Recent research related to carbon nanotubes, graphene and graphene analogous low-dimensional materials (Silicene, MoS2, WS2) have sparked tremendous interests in nanoscale sciences due to their promising applications associated with thermoelectrics and electronics. Heat conduction in these nanomaterials occurs by lattice vibration where energy is transmitted by interaction with neighboring atoms in a spring-like oscillating motion. As a result, quantized lattice vibrational elastic waves called phonons are emitted, which are the main contributors to heat conduction in these non-metallic nanomaterials. In analogous two-dimensional (2D) nanomaterials like graphene and silicene, thermal transport is mainly governed by three acoustic phonon modes (lattice vibration): in-plane longitudinal modes, in-plane transverse modes and out-of-plane vibrational modes. However, in carbon nanotubes there are four phonon modes contributing to the heat transport: longitudinal acoustic modes corresponding to the motion of atoms along the axis of the tube, two transverse degenerate modes and a twist mode. Out of all these modes, generally the low frequency, long-range modes are the ones which exert a dominant contribution towards heat transfer whereas high frequency, short-range modes have a very limited contribution to the thermal transport process. Literature contains inconsistent results identifying the dominant vibrational modes for these nanomaterials. In our research we explore this for carbon nanotubes, graphene and silicene. A clear understanding of the transport mechanism can enable design of novel nanomaterials that can be successfully used for targeted applications in thermal management. We have considered nanomaterials with varying dimensions and shape (carbon nanotube and graphene) and also nanostructures with varying isotope substitution but similar geometries (graphene and silicene).

Using classical molecular dynamics simulations, we identify the delocalized transverse modes in carbon nanotubes and out-of-plane flexural modes in graphene as the dominant modes which contribute mostly to the thermal transport in them. We extend our investigation to analogous 2D materials, graphene and silicene. Even though they are structurally similar, their heat conduction mechanisms are found to vary drastically. In contrast to the dominant out-of-plane flexural modes in graphene, the heat conduction in silicene occurs predominantly due to in-plane transverse acoustic modes. Due to the buckled silicene structure, coupling of the out-of-plane flexural modes and in-plane longitudinal modes causes a mode softening effect. The weaker Si-Si bond strength implies low group velocity of the out-of-plane phonons making them essentially non-existent for silicene. But despite the differences in the phonon modes, the variation in k with increasing isotope substitution in both graphene and silicene are found to be similar. The shift in vibrational spectra towards lower frequencies indicating the reduced energy carrying capacity of phonons due to mass disorder is found to be consistent in silicene too. Our results showing decrease in k in graphene and silicene compared well with an analytical model based on mean-field approximation. We hope that our study will initiate many more fascinating researches in this rapidly evolving area.