Title: Visualizing Ordered Electronic States in Epitaxial Graphene
Description: Since its physical isolation via the "scotch tape method," graphene (a monolayer of graphite) has attracted much attention from both the solid-state and high-energy scientific communities because its elementary excitations mimic relativistic chiral fermions. This has allowed graphene to act as a testbed for exploring exotic forms of symmetry breaking and for verifying certain longstanding theoretical predictions dating back to the very first formulation of relativistic quantum mechanics. In this dissertation I describe scanning tunneling microscopy and spectroscopy experiments that visualize ordered electronic states in graphene that originate from its unique chiral structure. Two detailed investigations of chemical vapor deposition graphene grown on copper are presented. In the first, a heretofore unrealized phase of graphene with broken chiral symmetry called the Kekulé distortion is directly visualized. In this phase, the graphene bond symmetry breaks and manifests as a (√3×√3)R30° charge density wave.

I show that its origin lies in the interactions between individual vacancies ("ghost adatoms") in the crystalline copper substrate that are mediated electronically by the graphene. These interactions induce the formation of a hidden order in the positions of the ghost adatoms that coincides with Kekulé bond order in the graphene itself. I then show that the transition temperature for this ordering is 300K, suggesting that Kekulé ordering occurs via enhanced vacancy diffusion at high temperature. In the second, Klein tunneling of electrons is visualized for the first time. Here, quasi-circular regions of the copper substrate underneath graphene act as potential barriers that can scatter and transmit electrons. At certain energies, the relativistic chiral fermions in graphene that Klein scatter from these barriers are shown to fulfill resonance conditions such that the transmitted electrons become trapped and form standing waves. These resonant modes are visualized with detailed spectroscopic images with atomic resolution that agree well with theoretical calculations.

The trapping time is shown to depend critically on the angular momenta quantum number of the resonant state and the radius of the trapping potential, with smaller radii displaying the weakest trapping.