Real-space mapping of magnetically quantized graphene states

The symmetry of graphene's two carbon sublattices underlies its unique electronic structure and half-integer quantum Hall effect. Quantized Hall resistance requires confinement of cyclotron orbits (Landau levels) in the sample interior. Such magnetic localization may be unique in graphene, especially for the fourfold-degenerate Landau level (LL(0)) straddling graphene's charge-neutrality energy. Here we map the two-dimensional spatial distribution of LL(0), using cryogenic scanning tunnelling spectroscopy to measure the local density of states (LDOS) on electronically decoupled multilayer epitaxial graphene. Unlike disordered LDOS patterns found in conventional quantum Hall systems, we find an organized pattern of localized states and extended states that emerge above a threshold magnetic field. In distinct regions, an energy gap associated with lattice-scale variations of the LDOS suggests the sublattice (and LL(0) valley) degeneracy is locally lifted. We propose this occurs when cyclotron orbits become small enough to sample regions of small symmetry-breaking potential originating from a graphene-on-graphene moire.