1 research outputs found
Local density of states and scanning tunneling currents in graphene
We present exact analytical calculations of scanning tunneling currents in
locally disordered graphene using a multimode description of the microscope
tip. Analytical expressions for the local density of states (LDOS) are given
for energies beyond the Dirac cone approximation. We show that the LDOS at the
and sublattices of graphene are out of phase by implying that the
averaged LDOS, as one moves away from the impurity, shows no trace of the
(with the Fermi momentum) Friedel modulation. This means that a
STM experiment lacking atomic resolution at the sublattice level will not be
able of detecting the presence of the Friedel oscillations [this seems to be
the case in the experiments reported in Phys. Rev. Lett. {\bf 101}, 206802
(2008)]. The momentum maps of the LDOS for different types of impurities are
given. In the case of the vacancy, features are seen in these maps. In
all momentum space maps, and features are seen. The
features are different from what is seen around zero momentum. An
interpretation for these features is given. The calculations reported here are
valid for chemical substitution impurities, such as boron and nitrogen atoms,
as well as for vacancies. It is shown that the density of states close to the
impurity is very sensitive to type of disorder: diagonal, non-diagonal, or
vacancies. In the case of weakly coupled (to the carbon atoms) impurities, the
local density of states presents strong resonances at finite energies, which
leads to steps in the scanning tunneling currents and to suppression of the
Fano factor.Comment: 21 pages. Figures 6 and 7 are correctly displayed in this new versio