Negative electronic compressibility in charge islands in twisted bilayer graphene

We report on the observation of negative electronic compressibility in twisted bilayer graphene for Fermi energies close to insulating states. To observe this negative compressibility, we take advantage of naturally occurring twist-angle domains that emerge during the fabrication of the samples, leading to the formation of charge islands. We accurately measure their capacitance using Coulomb oscillations, from which we infer the compressibility of the electron gas. Notably, we not only observe the negative electronic compressibility near correlated insulating states at integer filling, but also prominently near the band insulating state at full filling, located at the edges of both the flat and remote bands. Furthermore, the individual twist-angle domains yield a well-defined carrier density, enabling us to quantify the strength of electronic interactions and verify the theoretical prediction that the inverse negative capacitance contribution is proportional to the average distance between the charge carriers. A detailed analysis of our findings suggests that Wigner crystallization is the most likely explanation for the observed negative electronic compressibility.