Measuring the local quantum capacitance of graphene using a strongly coupled graphene nanoribbon

We present electrical transport measurements of a van-der-Waals heterostructure consisting of a graphene nanoribbon separated by a thin boron nitride layer from a micron-sized graphene sheet. The interplay between the two layers is discussed in terms of screening or, alternatively, quantum capacitance. The ribbon can be tuned into the transport gap by applying gate voltages. Multiple sites of localized charge leading to Coulomb blockade are observed, in agreement with previous experiments. Due to the strong capacitive coupling between the ribbon and the graphene top layer sheet, the evolution of the Coulomb blockade peaks in gate voltages can be used to obtain the local density of states and therefore the quantum capacitance of the graphene top layer. Spatially varying density and doping are found, which are attributed to a spatial variation of the dielectric due to fabrication imperfections.