In this paper, heat flux in graphene nanoribbons has been studied by using molecular dynamics simulations. It is found that the heat flux runs preferentially along the direction of decreasing width, which demonstrates significant thermal rectification effect in the asymmetric graphene ribbons. The dependence of rectification ratio on the vertex angle and the length are also discussed. Compared to the carbon nanotube based one-dimensional thermal rectifier, graphene nanoribbons have much higher rectification ratio even in large scale. Our results demonstrate that asymmetric graphene ribbon might be a promising structure for practical thermal (phononics) device.

We study thermal properties of one-dimensional (1D) harmonic and anharmonic lattices with a mass gradient. It is found that a temperature gradient can be built up in the 1D harmonic lattice with a mass gradient due to the existence of gradons. The heat flow is asymmetric in anharmonic lattices with a mass gradient. Moreover, in a certain temperature region, negative differential thermal resistance is observed. Possible applications in constructing thermal rectifiers and thermal transistors by using the graded material are discussed.

With molecular dynamics simulations, we demonstrate very obvious thermal rectification in large temperature range from 200 to 400 K in nanocone. We also observe that the rectification of nanocone does not depend on the length very sensitively, which is in stark contrast with the nanotube thermal rectifier in which the rectification decreases dramatically as the length increases. Our work demonstrates that carbon nanocone is a promising practical phononic device.