Quantum Hall transport as a probe of capacitance profile at graphene edges

The quantum Hall effect is a remarkable manifestation of quantized transport in a two-dimensional electron gas (2DEG). Given its technological relevance, it is important to understand its development in realistic nanoscale devices. In this work, we present how the appearance of different edge channels in a field-effect device is influenced by the inhomogeneous capacitance profile existing near the sample edges, a condition of particular relevance for graphene. We apply this practical idea to experiments on high quality graphene, demonstrating the potential of quantum Hall transport as a spatially resolved probe of density profiles near the edge of this two-dimensional electron gas.