Master Degree / Yüksek Lisans Tezleri

Permanent URI for this collectionhttps://hdl.handle.net/11147/3008

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Author: search.filters.author.Güçlü, Alev DevrimSubject: search.filters.subject.Graphene quantum dots

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  • Master Thesis
    Coulomb Impurities in Graphene Quantum Dots in a Magnetic Field
    (01. Izmir Institute of Technology, 2021) Eren, İsmail; Güçlü, Alev Devrim
    In this thesis, we investigate the atomic collapse of Graphene Quantum Dots (GQDs) in a magnetic field with the tight-binding (TB) model and mean-field Hubbard (MFH) approximation. We placed a charged impurity at the center of GQDs, and we systematically investigated the atomic collapse effect in the magnetic field by adjusting the charge of the impurity, size of the quantum dots, and magnitude of the magnetic field. It is shown that the electronic state with the lowest energy of Graphene resembled the same effect of the lowest bound state (TLBS) of atomic collapse. We confirmed the earlier findings, and we showed that the required critical charges of TLBS of the GQDs to collapse below the Fermi level are almost equal. Additionally, we investigate the formation of resonance states of GQDs, and among these resonance states, we study the evolution of the first-formed resonance state (R1). Applying a perpendicular magnetic field to GQD, decreased the critical charge of each structure, and we found that the decrease is dependent on the dot size. Moreover, we also found that TLBS of GQDs of varying sizes are crossed each other at a particular impurity charge and energy. We used the relation between the magnetic field and magnetic length (lB), and we compared B with the radius of the GQD (RGQD) in varying sizes. We found that TLBS of a GQD still converges to a particular crossing point (in terms of impurity charge and energy) as in no magnetic field when lB > RGQD. However, TLBS of a GQD diverges from the crossing point when lB < RGQD. It is studied that the continuum form of the R1 state became a chain of separated Landau levels in a magnetic field. Here we show that Landau level formation is more noticeable, and the inter-level separation of the Landau levels becomes more prominent when the lB < RGQD. Lastly, we investigated the atomic collapse of the Hofstadter's butterflies in GQDs. We found that increasing the impurity charge collapsed the energy levels. Also, increasing the impurity charge decreased (increased) the local density of states of the impurity center at the top (bottom) part of the spectrum of the Hofstadter's butterflies.
  • Master Thesis
    Disorder Induced Electronic and Magnetic Properties of Graphene Quantum Dots
    (Izmir Institute of Technology, 2019) Kul, Erdoğan Kul; Güçlü, Alev Devrim
    In this thesis, we aim to study magnetic properties of hexagonal shaped graphene quantum dots with armchair edge in the case of atomic collapse by modelling two vacancies on it. The measured relativistic electron transport property of the graphene allows us to observe the phenomenon called "atomic collapse" in a small energy scale which existence is proven theoretically before for atoms whose atomic number is higher than 170. First we modelled a Coulomb potential at the center of a hexagonal shaped and armchair edged GQD and examined by using tight-binding method. We obtain similar results with previous works. After that, we started to study magnetic properties of the dot by meanfield Hubbard method which includes spins into calculation. We modelled a vacancy close to the center of the dot and examined electronic and magnetic properties by MFH metod. Also we modelled two vacancies on the dot that we changed the distance between them and the direction respectively. Also by applying Coulomb potential at the center of the vacancies we examined magnetic behaviour at the atomic collapse regime. Also, we compared our results with the works obtained by using RKKY (Ruderman-Kittel- Kasuya-Yosida) interaction method which considers the indirect interactions of magnetic impurities that uses electrons of metallic substrates. We found that increasing Coulomb potential and increasing distance between the vacancies, reduces correlations of electrons around the vacancies. The ground state energy difference between ferromagnetic and antiferromagnetic systems, that proportional to interaction strength, shows similar behaviour that has been observed by using RKKY method. Also if we take out two atoms from the same sublattice and with the same spin property, changing Coulomb potential leads to ferromagnetic-anti-ferromagnetic phase transition, independent from the atomic collapse behaviour. Also we observed that there is no direct link between the magnetic transition and the energy difference of the vacancy states.