UC Riverside

Graphene consists of an atom-thick layer of carbon atoms arranged in a honeycomb lattice, and its low-energy electronic excitations are well described as massless Dirac fermions with spin half and an additional pseudospin degree of freedom. Impurities in graphene can have a significant effect on the local electronic structure of graphene when the Fermi level is near the Dirac point. We study the local electronic spectra and real-space and k-space local density of state (LDOS) maps of graphene with different impurities (diagonal and non-diagonal impurity potential) such as vacancies, substitutional impurities, and adatoms. In the presence of a perpendicular magnetic field, we use a linearization approximation for the energy dispersion and employ a $T$-matrix formalism to calculate the Green's function. We investigate the effect of an external magnetic field on the Friedel oscillations and impurity-induced resonant states.

Using a multimode description for an scanning tunneling microscope (STM) tip, we calculate STM currents for the substitutional and vacancies case and find that strong resonances in the LDOS at finite energies lead to the presence of steps in the STM current and suppression of the Fano factor. We also describe in detail the theory of scanning tunneling spectroscopy in graphene in the presence of adatoms, magnetic or not, with localized orbitals of arbitrary symmetry, corresponding to any given angular momentum state.We show that quantum interference effects

which are naturally inbuilt in the honeycomb lattice, in combination

with the orbital symmetry of the localized state, allow scanning tunneling

probes to characterize adatoms and defects in graphene.