  Step junctions are often present in layered materials, i.e. where
single-layer regions meet multi-layer regions, yet their effect on thermal
transport is not understood to date. Here, we measure heat flow across graphene
junctions (GJs) from monolayer to bilayer graphene, as well as bilayer to
four-layer graphene for the first time, in both heat flow directions. The
thermal conductance of the monolayer-bilayer GJ device ranges from ~0.5 to
9.1x10^8 Wm-2K-1 between 50 K to 300 K. Atomistic simulations of such GJ device
reveal that graphene layers are relatively decoupled, and the low thermal
conductance of the device is determined by the resistance between the two
dis-tinct graphene layers. In these conditions the junction plays a negligible
effect. To prove that the decoupling between layers controls thermal transport
in the junction, the heat flow in both directions was measured, showing no
evidence of thermal asymmetry or rectification (within experimental error
bars). For large-area graphene applications, this signifies that small bilayer
(or multilayer) islands have little or no contribution to overall thermal
transport.
