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The quantum Hall effect is a remarkable manifestation of quantized transport in a two-dimensional electron gas. 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.
The unique capabilities of capacitance measurements in bilayer graphene enable probing of layer-specific properties that are normally out of reach in transport measurements. Furthermore, capacitance measurements in the top-gate and penetration field
We demonstrate experimentally that graphene quantum capacitance $C_{mathrm{q}}$ can have a strong impact on transport spectroscopy through the interplay with nearby charge reservoirs. The effect is elucidated in a field-effect-gated epitaxial graphen
The structure of edge modes at the boundary of quantum Hall (QH) phases forms the basis for understanding low energy transport properties. In particular, the presence of ``upstream modes, moving against the direction of charge current flow, is critic
We study the effect of backward scatterings in the tunneling at a point contact between the edges of a second level hierarchical fractional quantum Hall states. A universal scaling dimension of the tunneling conductance is obtained only when both of
The quantum localization in the quantum Hall regime is revisited using Graphene monolayers with accurate measurements of the longitudinal resistivity as a function of temperature and current. We experimentally show for the first time a cross-over fro