Browsing by Subject "Disordered systems"
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Item Open Access First-principles study on structural, vibrational, elastic, piezoelectric, and electronic properties of the Janus BiXY (X= S, Se, Te and Y = F, Cl, Br, I) monolayers(American Physical Society, 2021-03-09) Varjovi, Mirali Jahangirzadeh; Durgun, EnginBroken inversion symmetry in atomic structure can lead to the emergence of specific functionalities at the nanoscale. Therefore, realizing 2D materials in Janus form is a growing field, which offers unique features and opportunities. In this paper, we investigate the structural, vibrational, elastic, piezoelectric, and electronic properties of Janus BiXY (X=S, Se, Te and Y=F, Cl, Br, I) monolayers based on first-principle methods. The structural optimization and vibrational frequency analysis reveal that all of the proposed structures are dynamically stable. Additionally, ab initio molecular dynamics simulations verify the thermal stability of these structures even at elevated temperatures. The mechanical response of the Janus BiXY crystals in the elastic regime is investigated in terms of in-plane stiffness and the Poisson ratio, and the obtained results ascertain their mechanical flexibility. The piezoelectric stress and strain coefficient analysis demonstrates the appearance of strong out-of-plane piezoelectricity, which is comparable with the Janus transition metal dichalcogenide monolayers. The calculated electronic band structures reveal that except for BiTeF, all Janus BiXY monolayers are indirect band gap semiconductors, and their energy band gaps span from the infrared to the visible part of the optical spectrum. Subsequently, large Rashba spin splitting is observed in electronic band structures when the spin-orbit coupling is included. The obtained results point out Janus 2D BiXY structures as promising materials for a wide range of applications in nanoscale piezoelectric and spintronics fields.Item Open Access Reentrant localization transition in a quasiperiodic chain(American Physical Society, 2021-03-09) Roy, S.; Mishra T., T.; Tanatar, Bilal; Basu S., S.Systems with quasiperiodic disorder are known to exhibit a localization transition in low dimensions. After a critical strength of disorder, all the states of the system become localized, thereby ceasing the particle motion in the system. However, in our analysis, we show that in a one-dimensional dimerized lattice with staggered quasiperiodic disorder, after the localization transition, some of the localized eigenstates become extended for a range of intermediate disorder strengths. Eventually, the system undergoes a second localization transition at a higher disorder strength, leading to all states being localized. We also show that the two localization transitions are associated with the mobility regions hosting the single-particle mobility edges. We establish this reentrant localization transition by analyzing the eigenspectra, participation ratios, and the density of states of the system.Item Open Access A study of the modern theory of polarization on extensions of one dimensional topological insulators and disordered systems(Bilkent University, 2021-12) Parlak, SelçukWe work on identifying topological and quantum phase transition via the modern theory of polarization. We go through the problem of electrostatics definition of absolute polarization via a discrete chain of anions and cations. We move from this discrete approach to a continuous one and prove the emergence of the Berry phase under adiabatic evolution. Introducing the Resta's position operator, we show the correspondence to the definition of polarization and go through the polarization distribution of the system. Using these concepts we studied band structures, topological invariants, and symmetries in the Su-Schrie er-Heeger model. With these basics, we analyzed the emergence of torus knots and its identification of topological transition on the distance-dependent SSH model. We go through the formal definitions of knot theory and how to identify them to establish a new system using Klein bottle knots. Following the distance vector structure in the distance-dependent SSH model, we try to establish a real-life system using Klein bottle parametrizations; Pinched torus, figure 8, and the bottle shape. In all of the parametrizations, the interpretation of the real-life system had hoppings on empty sites. Klein bottle knots are tried to observe via parametrizations of the Klein bottle. In all cases, due to the four-dimensional nature of the Klein bottle, we encountered intersecting curves on 3-dimensional interpretations of the Klein bottle. To understand the system better, we go through the Berry phase and dispersion relation of the system. After not encountering anything significant, we try to acquire a knot structure on fundamental polygons. We obtain a Hopf link and unlink with a possible intersection point. The intersection becomes hard to judge due to computational approximation on determining the knot diagrams. Due to the complexity of the project, we go through the Anderson model to study the modern theory of polarization. A background on Anderson localization with a computational method: Transfer matrix method is given. We state Mott's relation of conductivity and discuss the concept of mobility edge. We show the localization theory of Resta by introducing the complex number z. With this, we prove that the jzj becomes 1 when the states are localized and 0 when we have extended states. We also go through the scaling theory of localization. To understand the scaling theory, we introduce the concept of the renormalization group and discuss how this idea is used in the gang of four paper. We go through the assumptions and results of the gang of four by observing that the scaling exponent of conductance exhibits a critical value only in the three dimensions. Using Resta's quantity, we try to establish the gang of four results by examining the size scaling of the variance of polarization of the system and introducing a renormalization flow with Resta's quantity. We observe the low-temperature limit by examining a single state in the ground state. With this, we recover the results of the gang of four. Based on the discussion of Mott's on mobility edge, we further examine the high-temperature limit, where the system is in the average of all states. We identify the transition point via two fixed points(repulsive and attractive) on flow diagrams and size scaling exponent in all dimensions. We recover the behavior of the gang of four in one and three dimensions by examination of the fixed points, and we state the ambiguity of two-dimensional solutions due to the convergence problem of the fixed points. We further solidify the analogy of conductance and Resta's number by observing the Binder cumulant and analogical mobility edge of the system. We found the same repulsive fixed point on Binder cumulant and analogical behavior on the mobility edge argument.