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Thermal transport in graphene and graphene nanostructures have been studied experimentally and theoretically. Methods and previous work to measure and calculate the thermal conductivities of graphene and related nanostructures are briefly reviewed. We demonstrate that combining Raman spectroscopy for thermometry and electrical transport for Joule heating is an effective approach to measure both graphene thermal conductivity and graphenesubstrate interface thermal resistance. This technique has been applied to a variety of exfoliated or CVD-grown graphene samples (both suspended and substrate-supported), yielding values comparable with those measured using all-optical or all-electrical techniques. We have also employed classical molecular dynamics simulation to study thermal transport in graphene nanostructures and suggest such structures may be used as promising building blocks for nanoscale thermal engineering.

We have performed scanning gate microscopy (SGM) on graphene field effect transistors (GFET) using a biased metallic nanowire coated with a dielectric layer as a contact mode tip and local top gate. Electrical transport through graphene at various back gate voltages is monitored as a function of tip voltage and tip position. Near the Dirac point, the response of graphene resistance to the tip voltage shows significant variation with tip position, and SGM imaging displays mesoscopic domains of electron-doped and hole-doped regions. Our measurements reveal substantial spatial fluctuation in the carrier density in graphene due to extrinsic local doping from sources such as metal contacts, graphene edges, structural defects and resist residues. Our scanning gate measurements also demonstrate graphene's excellent capability to sense the local electric field and charges.