# Electronic Compressibility of Magic-Angle Graphene Superlattices

## TL;DR

This paper presents the first electronic compressibility measurements of magic-angle twisted bilayer graphene, revealing new insights into its interaction-driven ground state, energy gaps, and mini-bandwidth, with notable electron-hole asymmetry and field dependence.

## Contribution

It introduces the first capacitance-based compressibility measurements of magic-angle graphene, providing new data on energy gaps, mini-bandwidth, and field effects not accessible through previous methods.

## Key findings

- Large energy gaps at quarter- and half-filling in electron-doped regime
- Mini-bandwidth of approximately 35 meV wider than theoretical estimates
- Significant differences between compressibility and transport measurements in magnetic fields

## Abstract

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 chemical potential as a function of carrier density and find the widths of the energy gaps at fractional filling of the moir\'{e} 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 $\mathord{\sim}35\,\textrm{meV}$ mini-bandwidth 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.