Real-Space Imaging of Alternate Localization and Extension of Quasi   Two-Dimensional Electronic States at Graphite Surfaces in Magnetic Fields
  We measured the local density of states (LDOS) of a quasi two-dimensional (2D) electron system near point defects on a surface of highly oriented pyrolytic graphite (HOPG) with scanning tunneling microscopy and spectroscopy. Differential tunnel conductance images taken at very low temperatures and in high magnetic fields show a clear contrast between localized and extended spatial distributions of the LDOS at the valley and peak energies of the Landau level spectrum, respectively. The localized electronic state has a single circular distribution around the defects with a radius comparable to the magnetic length. The localized LDOS is in good agreement with a spatial distribution of a calculated wave function for a single electron in 2D in a Coulomb potential in magnetic fields. 
Y. Niimi, H. Kambara, T. Matsui, D. Yoshioka, and Hiroshi Fukuyama