  Prior ultralow thermal conductivity materials are not suitable for
thermoelectric applications due to the limited electronic transport in the
materials. Here, we present a new class of ultralow thermal conductivity
materials with substantial electronic heat transport. Our samples are
graphene/metal heterostructures of transferred graphene and ultrathin metal
films (Pd, Au and Ni) deposited by either thermal evaporation or rf magnetron
sputtering. For the evaporated samples, we achieve an ultralow thermal
conductivity of 0.06 W m-1 K-1, with phonons as the dominant heat carriers. The
ultralow thermal conductivity is due to a huge disparity in phonon energy in
graphene and metals. Interestingly, for the sputtered samples, we find that
about 50 % of heat is carried by electrons, even when thermal conductivity is
about 0.1 W m-1 K-1. We attribute the electronic contribution to transmission
of electrons across atomic-scale pinholes in graphene. With the ultralow
thermal conductivity and substantial electronic transport, the new materials
could be explored for thermoelectric applications.
