Electronic Compressibility of Magic-Angle Graphene Superlattices

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 moire 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 similar to 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.