Graphene’s unique massless electron behavior is observed in multilayer epitaxial graphene grown from SiC on the (0001¯) face. These fermions collapse into cyclotron orbits (Landau levels) when graphene is placed into a high magnetic field, B. The Landau levels are shown to follow a [special characters omitted] energy dependence, where N is the quantum number of the Landau level. Cryogenic ultra-high vacuum scanning tunneling microscopy (STM) and spectroscopy (STS) are performed to study the local behavior of these cyclotron states near defects. A new STS technique was designed where conductance measurements were performed while the magnetic field was changed. This technique allows for a direct measurement of the energy versus momentum relationship for graphene.

These measurements produced results which indicate a local doping effect due to the STM tip. Techniques relying on degenerate perturbation theory for graphene states solved in the symmetric gauge are shown to reliably model these effects. This perturbation method allows for the study of local nanometer scale screening effects in graphene, and indicates that the local tip effect can be modeled as a defect potential. Measurements of Landau levels (LLs) will be shown to depend on the combined potential of the tip induced band bending (TIBB) potential and local defect potentials. In addition magnetically localized defect states are presented. These are not explained by TIBB. The defect states are argued to be Stark shifted in energy by TIBB, eventually crossing the Fermi energy, E_f. Once states cross E_f further doping effects from the tip are measured. This switch from hole to electron state is also shown to change the local potential of the system which indicates a direct charge state of the defect, which modifies the local density of states.