Dimension dependence of negative differential thermal resistance in graphene nanoribbons

Negative differential thermal resistance (NDTR) in approximate graphene nanoribbons (GNRs) is investigated from one dimension to three dimensions by using classical molecular dynamics method. For single-layer GNRs, NDTR can not be observed for very narrow GNRs (one dimension), NDTR appears when the width of GNRs increases (two dimensions). However, NDTR disappears gradually on further increasing the width. For multiple-layer GNRs, when the number of the layers increases, GNRs becomes from two-dimensional system to three-dimensional system, NDTR regime reduces and eventually disappears. In addition, when the length of GNRs increases, NDTR regime also reduces and vanishes in the thermodynamic limit. These effects may be useful for designing thermal devices where NDTR plays an important role.