Thermal rectification in two- and three-dimensional segmented mass-graded anharmonic oscillator lattices with a ballistic spacer

The thermal rectifier is an analog of the electrical rectifier, in which heat flux in a forward direction is larger than that in the reverse one. Due to this controllability of the heat flux the thermal rectifier is a promising device from both theoretical an applicational points of view. In this work we study the thermal rectification efficiency of a two- and three-dimensional (3D) segmented system consisting of a coupled nearest-neighbor harmonic oscillator lattice (ballistic spacer) and two diffusive leads (modeled by a substrate potential) attached to the lattice at both boundaries. At variance with the one-dimensional instance, the obtained rectification rapidly decays as the system width increases in the 3D instance, but quickly saturates for the two-dimensional (2D) one. We also perform a systematic analysis of various structural parameters that have influence on the rectification efficiency and determine that, under most circumstances, the performance is better in the 2D instance than in the 3D instance of the herein studied model.