Near-field microwave scanning probe imaging of conductivity inhomogeneities in CVD graphene.

We have performed near-field scanning microwave microscopy (SMM) of graphene grown by chemical vapor deposition. Due to the use of probe-sample capacitive coupling and a relatively high ac frequency of a few GHz, this scanning probe method allows mapping of local conductivity without a dedicated counter electrode, with a spatial resolution of about 50 nm. Here, the coupling was enabled by atomic layer deposition of alumina on top of graphene, which in turn enabled imaging both large-area films, as well as micron-sized islands, with a dynamic range covering a low sheet resistance of a metal film and a high resistance of highly disordered graphene. The structures of graphene grown on Ni films and Cu foils are explored, and the effects of growth conditions are elucidated. We present a simple general scheme for interpretation of the contrast in the SMM images of our graphene samples and other two-dimensional conductors, which is supported by extensive numerical finite-element modeling. We further demonstrate that combination of the SMM and numerical modeling allows quantitative information about the sheet resistance of graphene to be obtained, paving the pathway for characterization of graphene conductivity with a sub-100 nm special resolution.

Topology of two-dimensional turbulence.

Velocity differences in the direct enstrophy cascade of two-dimensional turbulence are correlated with the underlying flow topology. The statistics of the transverse and longitudinal velocity differences are found to be governed by different structures. The wings of the transverse distribution are dominated by strong vortex centers, whereas the tails of the longitudinal differences are dominated by saddles. Viewed in the framework of earlier theoretical work, this result suggests that the transfer of enstrophy to smaller scales is accomplished in regions of the flow dominated by saddles.