Local measurements of cyclotron states in graphene

Abstract

Multilayer epitaxial graphene has been shown to contain "massless Dirac fermions" and is believed to provide a possible route to industrial-scale graphene electronics. We used scanning tunneling microscopy (STM) and spectroscopy (STS) in high magnetic fields to obtain local information on these fermions. A new STS technique was developed to directly measure graphene's energy-momentum relationship and resulted in the highest precision measurement of graphene's Dirac cone. STS spectra similar to ideal graphene were observed, but additional anomalies were also found. Extra peaks and an asymmetry between electron and hole states were shown to be caused by the work function difference between the Iridium STM tip and graphene. This tip effect was extracted using modeled potentials and performing a least square fit using degenerate perturbation theory on graphene's eigenstates solved in the symmetric gauge. Defects on graphene were then investigated and magnetic field effects were shown to be due to a mixture of potential effect from defects and the tip potential. New defect states were observed to localize around specific defects, and are believed to interact with the STM tip by Stark shifting in energy. This Stark shift gives a direct measurement of the capacitive coupling between the tip and graphene and agrees with the modeled results found when extracting the tip potential.