Real-Space Imaging of Alternate Localization and Extension of Quasi Two-Dimensional Electronic States at Graphite Surfaces in Magnetic Fields

TL;DR

This study visualizes how electronic states in graphite surfaces alternate between localized and extended in magnetic fields, revealing detailed spatial distributions and confirming theoretical wave functions.

Contribution

It provides direct real-space imaging of localized and extended electronic states in a 2D electron system on graphite surfaces under magnetic fields, confirming theoretical models.

Findings

Localized states are circular around defects with radius matching magnetic length

Extended states show different spatial distribution at peak energies

LDOS patterns agree with theoretical wave functions for Coulomb potential in magnetic fields

Abstract

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.