Effect of varying the atomic bond stiffness in the heat baths to the thermal conductance of a graphene junction

Abstract

We simulate ballistic thermal transport due to phonons in a graphene junction by letting it interact with heat baths located at its edges and thereby exposing it to a temperature gradient. The bond stretching force constant for the left (L, heat source), central (C, graphene junction) and right (R, heat sink) regions should ideally be the same since they are all made out of graphene with interactions described by the same interatomic potential. But in an experiment, the graphene sheets acting as heat baths are mounted on silicon oxide while the graphene junction in the central region is suspended with a trench underneath it to reduce its coupling to the silicon substrate. In such a case, the force constants may vary from one region to the next. In this paper, we investigate the effect of varying the atomic bond stiffness in the heat baths to the calculated thermal conductance of a graphene junction using the nonequilibrium Green's function method. We find that varying the force constants do not have a significant effect as the junction becomes larger and approaches the bulk behavior. At small junctions, the finite-size effect becomes relevant.