Imaging Coulomb interactions and migrating Dirac cones in twisted graphene by local quantum oscillations

Flat band moir\'e graphene systems have emerged as a quintessential platform to investigate correlated phases of matter. A plethora of interaction-driven ground states have been proposed, and yet despite extensive experimental effort, there has been little direct evidence that distinguishes between the various phases, in particular near charge neutrality point. Here, we use a nanoscale scanning superconducting quantum interference device to image the local thermodynamic quantum oscillations in alternating-twist trilayer graphene at magnetic fields as low as 56 mT, which reveal ultrafine details of the density of states and of the renormalization of the single-particle band structure by Coulomb interactions. We find that the charging self-energy due to occupied electronic states, is critical in explaining the high carrier density physics. At half-filling of the conduction flat band, we observe a Stoner-like symmetry breaking, suggesting that it is the most robust mechanism in the hierarchy of phase transitions. On approaching charge neutrality, where the charging energy is negligible and exchange energy is dominant, we find the ground state to be a nematic semimetal which is favored over gapped states in the presence of heterostrain. In the revealed semimetallic phase, the flat-band Dirac cones migrate towards the mini-Brillouin zone center, spontaneously breaking the C_3 rotational symmetry. Our low-field local quantum oscillations technique presents an alluring avenue to explore the ground states of diverse strongly interacting van der Waals systems.