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We report the first electronic compressibility measurements of magic-angle twisted bilayer graphene. The evolution of the compressibility with carrier density offers insights into the interaction-driven ground state that have not been accessible in prior transport and tunneling studies. From capacitance measurements, we determine the chemical potential as a function of carrier density and find the widths of the energy gaps at fractional filling of the moiré lattice. In the electron-doped regime, we observe unexpectedly large gaps at quarter- and half-filling and strong electron-hole asymmetry. Moreover, we measure a ∼35  meV minibandwidth that is much wider than most theoretical estimates. Finally, we explore the field dependence up to the quantum Hall regime and observe significant differences from transport measurements.

We report on electronic transport measurements of dual-gated nanodevices of the low-carrier density topological insulator (TI) Bi_{1.5}Sb_{0.5}Te_{1.7}Se_{1.3}. In all devices, the upper and lower surface states are independently tunable to the Dirac point by the top and bottom gate electrodes. In thin devices, electric fields are found to penetrate through the bulk, indicating finite capacitive coupling between the surface states. A charging model allows us to use the penetrating electric field as a measurement of the intersurface capacitance C_{TI} and the surface state energy-density relationship μ(n), which is found to be consistent with independent angle-resolved photoemission spectroscopy measurements. At high magnetic fields, increased field penetration through the surface states is observed, strongly suggestive of the opening of a surface state band gap due to broken time-reversal symmetry.

We use a scanning capacitance probe to image transport in the quantum Hall system. Applying a dc bias voltage to the tip induces a ring-shaped incompressible strip (IS) in the 2D electron system (2DES) that moves with the tip. At certain tip positions, short-range disorder in the 2DES creates a quantum dot island in the IS. These islands enable resonant tunneling across the IS, enhancing its conductance by more than 4 orders of magnitude. The images provide a quantitative measure of disorder and suggest resonant tunneling as the primary mechanism for transport across ISs.

Using single electron capacitance spectroscopy, we study electron additions in quantum dots containing two potential minima separated by a shallow barrier. Analysis of the addition spectra in the magnetic field allows us to distinguish between electrons delocalized over the entire dot and those localized in either of the potential minima. We demonstrate that a high magnetic field abruptly splits up a low-density droplet into two smaller fragments, each residing in a potential minimum. An unexplained cancellation of electron repulsion between electrons in these fragments gives rise to paired electron additions.