Master Degree / Yüksek Lisans Tezleri
Permanent URI for this collectionhttps://hdl.handle.net/11147/3008
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Master Thesis Radiative and Topological Properties of One-Dimensional Atomic Chains(01. Izmir Institute of Technology, 2024) İyican, Arda Deniz; Çakır, Özgür; Çakır, Özgür; 04.05. Department of Pyhsics; 04. Faculty of Science; 01. Izmir Institute of TechnologyBu tezde, bir boyutlu, her birim hücresinde iki özdeş iki seviyeli atom bulunan bir diatomik zincirin topolojik ve vakum aracılı kolektif özellikleri incelenmiştir. Zincir üzerinde sabit sayıda uyarılmanın olduğu altuzayda, sistem, dissipatif etkileri dikkate alan non-Hermityen bir efektif Hamiltonyen ile tanımlanmaktadır. Zincirde tek bir uyarım varlığında, sonsuz bir zincir için kolektif radyatif davranış, öz durumları Bloch tipi durumlar olan etkin Hamiltoniyene karşılık gelen karmaşık enerji bantlarından ortaya çıkarılmıştır.Tek bir uyarıma sahip sonlu bir zincir için radyatif özellikler, sistemin etkin Hamiltonyeninin tam diyagonalizasyonuyla ortaya çıkarılmıştır. Altışınımlı durumların varlık koşulları belirlenmiştir. Ele alınan model, uzun menzilli etkileşimler ve dissipasyon nedeniyle genişletilmiş, non-Hermityen bir SSH modelidir. Bu sistem için topolojik özellikleri ortaya çıkarmak amacıyla kompleks Berry fazı hesaplanmış ve ardından topolojik olarak trivial olmayan durumlar için kenar durumları belirlenmiştir. Ayrıca, ışınımlı, altışınımlı ve topolojik kenar durumlarından gelen radyasyon desenleri, radyasyon bölgesindeki Poynting vektörünün hesaplanmasıyla gösterilmiştir.Master Thesis Electronic Transport in a Boundary-Driven One-Dimensional Chain With Bulk Dephasing(01. Izmir Institute of Technology, 2024) Yeler, Hakan; Çakır, Özgür; Çakır, Özgür; 04.05. Department of Pyhsics; 04. Faculty of Science; 01. Izmir Institute of TechnologyBu tezde, etkileşimli ve etkilemşimsiz fermiyonların bir boyutlu zincir üzerinde denge dışı durağan durumdaki taşınım özellikleri, çevre etkilerini de hesaba katarak incelenmiştir. Sistem dinamiği Lindblad master denklemi kullanılarak hesaplanmıştır. Taşınımı karakterize eden akım operatörü tanımlanmıştır. Hilbert uzayının eksponansiyel artış göstermesi sebebiyle, çok parçacıklı sistemlerin çözümünü hesaplamak zordur. Bu sebeple farklı çözüm metodları incelenmiştir. Hesaplama avantajlarından dolayı, etkileşimsiz sistemlerin çözümü için kovaryans matris methodu tanıtılmıştır. Etkileşimli sistemler için ortalama alan ve korelasyon fonksiyonların hiyerarşisi gibi yaklaşık metodlar tanıtılıp, birbirleriyle kıyaslanmıştır. Taşınımın davranışı kesin çözüm yöntemi yardımıyla incelenmiştir. Lindblad denklemi vektörize edilerek doğrusal denklem sistemi elde edilmiştir. Elde edilen doğrusal denklem sistemi, Python programlama dili kullanılarak çözülmüştür. Denge dışı durağan durum yoğunluk matrisi ve akım, farklı çevre parametrelerine göre hesaplanmıştır.Master Thesis Electronic Properties of Correlated Impurities in Two Dimensional Materials(01. Izmir Institute of Technology, 2023) Dolu, Volkan; Çakır, Özgür; Çakır, Özgür; 04.05. Department of Pyhsics; 04. Faculty of Science; 01. Izmir Institute of TechnologyThis Master's thesis investigates the effects of single and dual impurity potentials on the electronic properties of both pristine and gapped graphene, being examples of two-dimensional materials. The behavior of 2D materials at the atomic levels, particularly graphene, has been of interest due to their particular electronic properties, such as high electron mobility at certain conditions. The presence of impurities may significantly influence these properties, providing a modifiable platform for rearranging electronic characteristics for diverse applications. Our research focuses on how the impurity states that emerge, especially around energies at low DOS, affect the electronic structure and the interaction between the impurities. We study these effects in the presence of both single and dual impurity potentials of varied strength using computational models based on tight-binding approach. We begin by looking at how the single impurity potentials affect the electronic properties of pristine graphene and gapped graphene. We analyze the change in DOS and energy of the system, along with the identification of the impurity states, utilizing participation ratio for localization. Then, we extend our study to dual impurity potentials and their impacts to provide a knowledge of multi-impurity scenarios. We explore the interaction of the impurities mediated by the Fermi sea. In particular, we studied the hybridization of impurity states and corresponding impurity energies. Next, we determine the force arising between impurities for various Fermi energies, impurity-impurity distances and impurity potential strengths for graphene and gapped graphene.Master Thesis Entanglement and Topological Phenomena in Quantum Walks(01. Izmir Institute of Technology, 2023) Çakır, Özgür; Çakır, Özgür; 04.05. Department of Pyhsics; 04. Faculty of Science; 01. Izmir Institute of TechnologyQuantum walk, a counterpart of classical random walk, is widely used in the development of quantum algorithms and the modelling of physical systems. Since it has a simple and powerful mathematical structure, its implementation in physical systems serves to solve complex problems. In one-dimensional space, we investigated the topological properties of the simple quantum walk, and under which conditions the simple quantum walk possesses winding numbers. Then, we introduced the split-step quantum walk in a twodimensional space and numerically obtained Chern number phase diagram of each band as a function of rotation parameters. Subsequently, we introduced and studied the quantum walk protocols governed by two coins in a two-dimensional space. We first explored the entanglement and topological properties of a quantum walk protocol governed by a single non-local two-coin operator followed by translations along two spatial directions each governed by a different coin. We deduced that the motion reduces to one-dimensional motion in two spatial directions in decoupled coin subspaces. Then, we studied the split-step quantum walk protocols, where each step is comprised of local coin operations, followed by translations, non-local coin operations, and translations again. In these protocols, each step involves two translations along two spatial directions, and translations along a given spatial direction were either governed by the same coin or alternating coins. We also explored three different non-local coin operations, where a collective rotation takes place in a coin space conditioned on the state of the other coin's state along the same direction or perpendicular direction. We identified the effective Hamiltonian of the system and determined its eigenstates which are comprised of four bands in the Brillouin zone. For all the protocols we have introduced, we studied the coin-coin entanglement and topological properties as a function of coin rotation parameters.Master Thesis Electron Optics in Graphene(01. Izmir Institute of Technology, 2022) Çakır, Özgür; Çakır, Özgür; 04.05. Department of Pyhsics; 04. Faculty of Science; 01. Izmir Institute of TechnologyNegative refraction, also known as Veselago lensing, was first predicted by Victor Veselago in 1968 (Veselago (1968)). Its unique effect has a great potential for both scientific and technological applications such as superlenses. Unlike the conventional positive refractive index, focusing effect can be observed by negative refraction. In this thesis, the focusing effect was investigated theoretically through on n-p junction in graphene. The opposite chirality of electrons and holes enable the negative refraction where electrons( holes) have their momentum parallel(anti-parallel) to the group velocity. The case when potential barrier is directed perpendicular to KK direction, where K and K are the Dirac points were considered. The Green’s functions were calculated analytically and derived the susceptibility using the Green’s functions for various positions of the sources and the receiver at various Fermi energies. The spatial Green’s functions were calculated analytically and derived the static susceptibility (response function).Master Thesis B92 Based Quantum Key Distribution With Faint Pulsed Laser(01. Izmir Institute of Technology, 2021) Ateş, Serkan; Çakır, Özgür; Ateş, Serkan; Çakır, Özgür; 04.05. Department of Pyhsics; 04. Faculty of Science; 01. Izmir Institute of TechnologyIn quantum key distribution (QKD), photons are used to share the key between the transmitter and receiver, and in principle, single photon sources should be used to create a secure communication channel. Nowadays, attenuated laser sources are used in many studies. While it is practical to use attenuated laser pulses for QKD system, it poses many safety issues due to the possibility of multiple photons in the laser pulses. In addition, the key rate is waived to increase the level of security. However, the use of single photon sources is not as easy and practical as using attenuated laser sources. Today, studies of single photon sources to be used for QKD continue. In order for these single photon sources to be used actively, a photon source that operates at room temperature, operates in a wide band-gap range for different areas of use (underwater, optical fiber-based and free space) and can be excited at high speed is required. Since hBN defect centers are a material that can produce single photons at room temperature and have a wide band gap, it seems very ideal for these studies. In this thesis, studies have been carried out on the realization of the protocol, which is a part of QKD, with solid-state materials that produce single photons. In the studies, a key was produced with a faint pulsed laser. Also, data is encrypted using the key of the transmitter. Then the data is successfully decrypted with the key measured by the receiver.