Thermal rectification and negative differential thermal resistance in lattices with mass gradient

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.