Imaging field-tuned quantum Hall broken-symmetry orders and quantum Hall conducting channel in 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 magnetic fields1-22. A rich set of quantum Hall ferromagnetic (QHFM) phases with different lattice-scale symmetry-breaking orders are predicted to be realized in high magnetic fields when the 0LL in graphene is half filled1-8,13-16. Here we report a field-tuned continuous quantum phase transition of different valley orderings in QHFM of charge-neutral graphene on insulating tungsten diselenide (WSe2). The phase transition is clearly revealed by anomalous field-dependent energy gap in the half-filled 0LL. Via atomic resolution imaging of electronic wavefunctions during the phase transition, we observe microscopic signatures of field-tuned continuous-varied valley polarization and valley inversion, which are unexpected and beyond current theory predictions. Moreover, the topological quantum Hall conducting channel of the graphene is directly imaged when the substrate (WSe2) introduces band bending of the 0LL.