In the rst part of this thesis we discuss some details of properties of graphene
and we explain the tight-binding approach to nd the energy spectrum in graphene.
In the second part of the thesis, we solve a nonlinear integral equation for the electrostatic
potential in doped graphene due to an external charge, arising from a
Thomas-Fermi (TF) model for screening by graphene's electron bands. In particular,
we study the e ects of a nite equilibrium charge carrier density in graphene,
non-zero temperature, non-zero gap between graphene and a dielectric substrate,
as well as the nonlinearity in the band density of states. E ects of the exchange
and correlation interactions are also brie
y discussed for undoped graphene at zero
temperature. Results from the nonlinear model are compared with results from
both the linearized TF model and the dielectric screening model within the random
phase approximation (RPA). In addition, the image potential of the external charge
is evaluated from the solution of the nonlinear integral equation and compared to
the results of linear models. We have found generally good agreement between the
results of the nonlinear TF model and the RPA model in doped graphene, apart
from Friedel oscillations in the latter model. However, relatively strong nonlinear
e ects in the TF model are found to persist even at high doping densities and large
distances of the external charge.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/5098 |
| Date | 06 April 2010 |
| Creators | Ghaznavi, Mahmoudreza |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
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