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Thermal transport in a 2D stressed nanostructure with mass gradient

Inspired by some recent molecular dynamics (MD) simulations and experiments on suspended graphene nanoribbons, we study a simplified model where the atoms are disposed in a rectangular lattice coupled by nearest neighbor interactions which are quadratic in the interatomic distance. The system has a mechanical strain, and the border atoms are coupled to Langevin thermal baths. Atom masses vary linearly in the longitudinal direction, modeling an isotope or doping distribution. This asymmetry and tension modify thermal properties. Although the atomic interaction is quadratic, the potential is anharmonic in the coordinates. By direct MD simulations and solving Fokker--Planck equations at low temperatures, we can better understand the role of anharmonicities in thermal rectification. We observe an increasing thermal current with an increasing applied mechanical tension. The temperatures and thermal currents vary along the transverse direction. This effect can be useful to establish which parts of the system are more sensitive to thermal damage. We also study thermal rectification as a function of strain and system size.