Graphene exhibits extraordinary electronic and mechanical properties, and extremely high thermal conductivity. Being a very stable atomically thick membrane that can be suspended between two leads, graphene provides a perfect test platform for studyi
ng thermal conductivity in two-dimensional systems, which is of primary importance for phonon transport in low-dimensional materials. Here we report experimental measurements and non-equilibrium molecular dynamics simulations of thermal conduction in suspended single layer graphene as a function of both temperature and sample length. Interestingly and in contrast to bulk materials, when temperature at 300K, thermal conductivity keeps increasing and remains logarithmic divergence with sample length even for sample lengths much larger than the average phonon mean free path. This result is a consequence of the two-dimensional nature of phonons in graphene and provides fundamental understanding into thermal transport in two-dimensional materials.
Random networks of carbon nanotubes and metallic nanowires have shown to be very useful in the production of transparent, conducting films. The electronic transport on the film depends considerably on the network properties, and on the inter-wire cou
pling. Here we present a simple, computationally efficient method for the calculation of conductance on random nanostructured networks. The method is implemented on metallic nanowire networks, which are described within a single-orbital tight binding Hamiltonian, and the conductance is calculated with the Kubo formula. We show how the network conductance depends on the average number of connections per wire, and on the number of wires connected to the electrodes. We also show the effect of the inter-/intra-wire hopping ratio on the conductance through the network. Furthermore, we argue that this type of calculation is easily extendable to account for the upper conductivity of realistic films spanned by tunneling networks. When compared to experimental measurements, this quantity provides a clear indication of how much room is available for improving the film conductivity.
