Electronic structure of graphene under the influence of external fields

Ankara : The Department of Physics and the Graduate School of Engineering and Science of Bilkent University, 2012. ; Thesis (Ph. D.) -- Bilkent University, 2012. ; Includes bibliographical references leaves 106-112. ; 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 ...