Browsing by Subject "vacancies"
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Item Open Access Boron nitride and graphene 2D nanostructures from first-principles(Bilkent University, 2010) Ovalı, Rasim VolgaIn this thesis, the structures as well as mechanical and electronic properties of various boron nitride (BN) and graphene based two dimensional (2D) nano-structures are investigated in detail from rst-principle calculations using planewave pseudopotential method based on density functional theory. At the beginning of the thesis, essentials of the density functional theory (DFT) and a guidance for performing ab-initio calculations in the framework of DFT is presented. In addition, fundamentals about the exchange-correlation potential as well as approaches approximating it like local density approximation (LDA) and generalized gradient approximation (GGA) are discussed. Along with this thesis, rst of all, in order to understand the relation between the hexagonal boron nitride (h-BN) and cubic boron nitride (c-BN) and the growth of three dimensional (3D) BN structures, various defect structures introduce to BN monolayer, including point defects and especially highly curved defects such as n-fold rings, are investigated in detail. The calculated formation energies and structural analysis showed that 4-fold BN rings are the transient phase between h-BN to c-BN during c-BN nucleation. The charge density plots and density of states analysis further provide information about the electronic structure of these defect formations. Second of all, we have studied the formation of boron-nitride-carbon (BNC) ternary thin lms, so we observed the carbon nucleation in BN monolayer. These DFT based calculations show that carbon prefers the nitrogen site at rst step and the calculated defect energy indicates that carbon atoms tends to aggregate in BN hexagonal network, and hence increases the number of C-C bonds. BNC structures have magnetization of =1.0 B for odd number of carbon adsorption. Further substitution of carbon atoms into BN layer showed that carbon atomsform hexagonal rings instead of armchair or zigzag formations. Moreover, we calculated the vibrational modes of BN monolayer and BNC structures, and phonon density of states graphs are presented. The phonon frequencies intrinsic to C-C bond oscillations are observed, which is in good agreement with the experiment. Finally, point defects and ring formations on graphene are investigated in order to understand the Y-junction and kink formation in carbon nanotubes (CNTs). Pentagonal rings are the good candidates to initiate such 2D networks in CNTs. The curvature increases with increasing number of pentagonal rings. Moreover, interaction of sulphur atoms with graphene defects is studied. Final geometries and binding energies suggest that sulphur prefers to adsorb on defected regions, but it is not responsible for the formation of these structures or defects.Item Open Access Electronic structure of graphene under the influence of external fields(Bilkent University, 2012) İslamoğlu, SelcenIn 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.