| Local studies of correlated electron systems by scanning tunneling microscopy (STM) are the subject of this thesis. We focus on two novel materials: the high-temperature superconductor Bi2Sr2YxCa 1--xCu2O8+delta and graphene, a two-dimensional host of massless Dirac fermions. We use a custom-built low-temperature, high-magnetic field, ultra-high vacuum STM to probe electron-boson correlation in a cuprate superconductor and to observe for the first time the Kondo effect with Dirac particles.;First, inelastic electron tunneling spectroscopy (IETS) is used as a way to identify local signatures of bosonic coupling in Bi2Sr 2YxCa1--xCu2O8+delta. A strong sideband feature is present in our tunneling spectroscopy measurements with a characteristic energy O ≥ 70 meV. Its shape and intensity prompted us to apply the fundamentals of IETS to describe this sideband in terms of a replica of the d-wave density of quasiparticle states, generated by a bosonic coupling. In doing so, we can invert the tunneling spectrum to extract the boson density of states, giving us access to its energy scale, coupling constant, and bandwidth. All signs point to a high-energy mode with a weak anti-correlation between O and Delta, the measured superconducting energy gap.;Next, we use Fourier-transform scanning tunneling microscopy and spectroscopy (FT-STM) as a technique to study quasiparticle scattering and interference in graphene. By accessing the wave-vectors of quantum interference patterns generated by scattering of quasiparticles off local impurities and defects, we can measure the dispersion relation of Dirac fermions in graphene. The Fourier-transforms also tell us about which symmetries are present in the electronic structure of graphene and we confirm that pseudospin is preserved when Dirac fermions scatter in epitaxial graphene.;Finally, we dope our sample with cobalt atoms to experimentally probe the physics of individual magnetic moments on graphene. Tunneling spectroscopy reveals sharp bimodal resonances over individual adatoms, consistent with an unconventional Kondo effect. Combining measurements of local density of states in a magnetic field and scattering patterns around impurities sheds light on the nature of these many-body ground states and their intricate connection to the underlying symmetries of graphene. |
