Imaging field-tuned quantum Hall broken-symmetry orders and the quantum Hall conducting channel in a charge-neutral graphene/WSe2 heterostructure

The zeroth Landau level (0LL) in graphene has emerged as a flat band platform in which distinct many-body phases can be explored with unprecedented control by simply tuning the strength and/or direction of the magnetic field. A rich set of quantum Hall ferromagnetic phases with different lattice-scale symmetry-breaking orders are predicted to be realized in high magnetic fields when the 0LL in graphene is half-filled. Here we report on a field-tuned continuous phase transition of different valley orderings in a quantum Hall ferromagnetic phase of charge-neutral graphene on insulating tungsten diselenide (WSe2). The phase transition is clearly revealed by an anomalous field-dependent energy gap in the half-filled 0LL. Using atomic resolution imaging of electronic wavefunctions during the phase transition, we unexpectedly observe the microscopic signatures of field-tuned continuous-varied valley polarization and valley inversion, which are beyond current theoretical predictions. Moreover, the quantum Hall conducting channel of the graphene is directly imaged when the substrate (WSe2) introduces band bending of the 0LL.