Electronic structure of graphene under the influence of external fields
Author
İslamoğlu, Selcen
Advisor
Gülseren, Oğuz
Date
2012Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
In this thesis, the electronic structure of graphene under the influence of external
fields such as strain or magnetic fields is investigated by using tight-binding
method. Firstly, we study graphene for a band gap opening due to uniaxial strain.
In contrast to the literature, we find that by considering all the bands (both σ
and π bands) in graphene and including the second nearest neighbor interactions,
there is no systematic band gap opening as a function of applied strain. Our results
correct the previous works on the subject. Secondly, we examine the band
structure and Hall conductance of graphene under the influence of perpendicular
magnetic field. For graphene, we demonstrate the energy spectrum in the
presence of magnetic field (Hofstadter Butterfly) where all orbitals are included.
We recover both the usual and the anomalous integer quantum Hall effects depending
on the proximity of the Dirac points for pure graphene and the usual
integer quantum Hall effect for pure square lattice. Then, we explore the evolution
of electronic properties when imperfections are introduced systematically
to the system. We also demonstrate the results for a square lattice which has a
distinct position in cold atom experiments. For the energy spectrum of imperfect
graphene and square lattice under magnetic field (Hofstadter Butterflies), we
find that impurity atoms with smaller hopping constants result in highly localized
states which are decoupled from the rest of the system. The bands associated
with these states form close to E = 0 eV line. On the other hand, impurity
atoms with higher hopping constants are strongly coupled with the neighboring
atoms. These states modify the Hofstadter Butterfly around the minimum and
maximum values of the energy and for the case of graphene they form two self
similar bands decoupled from the original butterfly. We also show that the bands
and gaps due to the impurity states are robust with respect to the second order
hopping. For the Hall conductance, in accordance with energy spectra, the localized
states associated to the smaller hopping constant impurities or vacancies do
not contribute to Hall conduction. However the higher hopping constant impurities
are responsible for new extended states which contribute to Hall conduction.
Our results for Hall conduction are also robust with respect to the second order
interactions.
Keywords
Graphenetight-binding method
point defects
vacancies
strain
magnetic field
Hofstadter Butterflies
Hall conductance
2D electronic systems