The zeroth Landau level of graphene under a magnetic field is a particularly interesting strongly interacting flat band because interelectron interactions are predicted to induce a rich variety of broken-symmetry states with distinct topological and lattice-scale orders. Evidence for these states comes mainly from indirect transport experiments that suggest that broken-symmetry states are tunable by boosting the Zeeman energy or by dielectric screening of the Coulomb interaction. In this talk, I will describe three distinct broken-symmetry phases in graphene that we have identified in transport and imaged using scanning tunneling spectroscopy [1]. I will also discuss the real-space structure of quantum Hall edge states that we found to be free of electrostatic reconstruction [2].

[1] A. Coissard et al. Nature 605, 51 (2022)

[2] A. Coissard et al. Science Adv. 9, eadf7220 (2023)