Thermal rectification in one-dimensional mass-graded lattices with an on-site potential

In this work we perform a systematic analysis of various structural parameters that have influence on the thermal rectification effect, i.e. asymmetrical heat flow, and the negative differential thermal resistance present in a one-dimensional anharmonic lattice with mass gradient and coupled to a substrate potential. For two different mass profiles ( linear and exponential) we compute the thermal conductivity as a function of the system size and determined that its value, computed with the system coupled to the substrate potential, is lower than the corresponding one without such potential for each system size, with a highest value of the divergence exponent corresponding to the exponential mass profile. The rectification efficiency is always higher for the linear mass-graded lattice in all the studied cases, whereas that of the exponential mass-graded one is largely insensitive to the variation, in the considered range of values, of the studied parameters. This latter type of lattice presents no negative differential thermal resistance in the low temperature regime whatsoever.