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dc.contributor.advisorGülseren, Oğuzen_US
dc.contributor.authorİslamoğlu, Selcenen_US
dc.date.accessioned2016-01-08T18:21:55Z
dc.date.available2016-01-08T18:21:55Z
dc.date.issued2012
dc.identifier.urihttp://hdl.handle.net/11693/15640
dc.descriptionAnkara : The Department of Physics and the Graduate School of Engineering and Science of Bilkent University, 2012.en_US
dc.descriptionThesis (Ph. D.) -- Bilkent University, 2012.en_US
dc.descriptionIncludes bibliographical references leaves 106-112.en_US
dc.description.abstractIn 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.en_US
dc.description.statementofresponsibilityİslamoğlu, Selcenen_US
dc.format.extentxvi, 112 leaves, illustrationsen_US
dc.language.isoEnglishen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectGrapheneen_US
dc.subjecttight-binding methoden_US
dc.subjectpoint defectsen_US
dc.subjectvacanciesen_US
dc.subjectstrainen_US
dc.subjectmagnetic fielden_US
dc.subjectHofstadter Butterfliesen_US
dc.subjectHall conductanceen_US
dc.subject2D electronic systemsen_US
dc.subject.lccTA418.9.N35 I74 2012en_US
dc.subject.lcshNanostructured materials.en_US
dc.subject.lcshGraphene.en_US
dc.subject.lcshGraphite.en_US
dc.titleElectronic structure of graphene under the influence of external fieldsen_US
dc.typeThesisen_US
dc.departmentDepartment of Physicsen_US
dc.publisherBilkent Universityen_US
dc.description.degreePh.D.en_US


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