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Real-space mapping of magnetically quantized graphene states

Nature Physics volume 6, pages 811–817 (2010)Cite this article

Abstract

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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Figure 1: Topographic STM images of the multilayer epitaxial graphene sample grown on SiC.
Figure 2: STS dI/dV maps showing an extended state at the LL0av peak energy (E0av) and localized states at energies above and below E0av.
Figure 3: Spatial variation of the LL0 energy and the local lifting of valley degeneracy.
Figure 4: Magnetic-field dependence of the spatially varying LL0 peak energy.
Figure 5: Energy-gap map and proposed model of the local valley splitting.

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Acknowledgements

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.

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Authors and Affiliations

  1. School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA

    David L. Miller, Kevin D. Kubista, Ming Ruan, Walt A. de Heer, Markus Kindermann & Phillip N. First

  2. Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA

    Gregory M. Rutter & Joseph A. Stroscio

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Contributions

D.L.M., K.D.K., G.M.R., P.N.F. and J.A.S. carried out the measurements in the 4 K UHV STM facility in the CNST at NIST. The graphene sample was grown by M.R. and W.A.dH at Georgia Tech, and the surface prepared/characterized by D.L.M. and P.N.F. A theoretical analysis of the epitaxial graphene multilayer system was carried out by M.K.

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Correspondence to Phillip N. First or Joseph A. Stroscio.

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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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