Visualizing interaction-driven restructuring of quantum Hall edge states

Many topological phases host gapless boundary modes that can be markedly modified by electronic interactions. Even for the long-studied edge modes of quantum Hall phases^1,2, forming at the boundaries of two-dimensional electron systems, the nature of such interaction-induced changes has been elusive. Despite advances made using local probes^3-13, key experimental challenges persist: the lack of direct information about the internal structure of edge states on microscopic scales, and complications from edge disorder. Here we use scanning tunnelling microscopy to image pristine electrostatically defined quantum Hall edge states in graphene with high spatial resolution and demonstrate how correlations dictate the structures of edge channels on both magnetic and atomic length scales. For integer quantum Hall states in the zeroth Landau level, we show that interactions renormalize the edge velocity, dictate the spatial profile for co-propagating modes and induce unexpected edge valley polarization, which differs from the bulk. Although some of our findings can be understood by mean-field theory, others show breakdown of this picture, highlighting the roles of edge fluctuations and inter-channel couplings. We also extend our measurements to spatially resolve the edge state of fractional quantum Hall phases and detect spectroscopic signatures of interactions in this chiral Luttinger liquid. Our study establishes scanning tunnelling microscopy as a promising tool for exploring the edge physics of the rapidly expanding group of two-dimensional topological phases, including recently realized fractional Chern insulators.