  Mapping the thermal transport properties of materials at the nanoscale is of
critical importance for optimizing heat conduction in nanoscale devices.
Several methods to determine the thermal conductivity of materials have been
developed, most of them yielding an average value across the sample, thereby
disregarding the role of local variations. Here, we present a method for the
spatially-resolved assessment of the thermal conductivity of suspended graphene
by using a combination of confocal Raman thermometry and a finite-element
calculations-based fitting procedure. We demonstrate the working principle of
our method by extracting the two-dimensional thermal conductivity map of one
pristine suspended single-layer graphene sheet and one irradiated using helium
ions. Our method paves the way for spatially resolving the thermal conductivity
of other types of layered materials. This is particularly relevant for the
design and engineering of nanoscale thermal circuits (e.g. thermal diodes).
