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 (LL0) straddling graphene’s charge-neutrality energy. Here we map the two-dimensional spatial distribution of LL0, 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 LL0 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 moiré.
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We thank C. Berger, M. Sprinkle, N. Sharma, S. Blankenship, A. Band and F. Hess for their technical contributions to this work. Financial support from NSF (DMR-0804908), the Semiconductor Research Corporation Nanoelectronics Research Initiative (NRI-INDEX) and the W. M. Keck Foundation are gratefully acknowledged. Graphene production facilities of the Georgia Tech MRSEC (NSF DMR-0820382) were employed.
The authors declare no competing financial interests.
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Miller, D., Kubista, K., Rutter, G. et al. Real-space mapping of magnetically quantized graphene states. Nature Phys 6, 811–817 (2010). https://doi.org/10.1038/nphys1736
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